Name:_________________ Honors geometry Review #1 for MP3 Exam 1. The line y 2x 3 is the perpendicular bisector of MN and intersects MN at ( 6, 9). Find an equation of HJJJG MN in point-slope form. 2. Explain why the triangles are similar and find DE. 3. Explain why the triangles are similar and find BC 4. Find DE. 5. Determine whether ΔABC and ΔDEF are similar. If so, write the similarity ratio and a similarity statement. 6. Given a right triangle with the length of one leg equal to 9 centimeters and the length of the hypotenuse equal to 15 centimeters, what is the length of the other leg? 7. If B and C are right angles, what additional congruence statement would allow you to prove DCB ABC by the ASA postulate? 8.Draw your own diagram A ladder is leaning against a building. The distance from the building to the bottom of the ladder is 7 feet. The ladder is 25 feet long. How high up the building is the top of the ladder? 9. WXYZ is a rhombus. What is m∠XYZ and m∠YZW 10. Which is a possible value of x? A 21 C 25 B 23 D 26
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Name:_________________ Honors geometry Review #1 for MP3 Exam 1.
Name ________________________________________ Date ___________________ Class __________________
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
UABC UDEF
Side-Side-Side (SSS) Similarity
If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar.
UABC UDEF
Side-Angle-Side (SAS) Similarity
If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.
UABC UDEF
Name ________________________________________ Date ___________________ Class __________________
Reteach Triangle Similarity: AA, SSS, and SAS continued
You can use AA Similarity, SSS Similarity, and SAS Similarity to solve problems. First, prove that the triangles are similar. Then use the properties of similarity to find missing measures.
Explain why UADE UABC and then find BC. Step 1 Prove that the triangles are similar. A A by the Reflexive Property of .
3 16 2
ADAB
2 14 2
AEAC
Therefore, UADE UABC by SAS . Step 2 Find BC.
AD DEAB BC
Corresponding sides are proportional.
3 3.56 BC
Substitute 3 for AD, 6 for AB, and 3.5 for DE.
3(BC) 6(3.5) Cross Products Property 3(BC) 21 Simplify. BC 7 Divide both sides by 3.
Explain why the triangles are similar and then find each length.
Foundations for Geometry Chapter Test Form C continued
10. The measure of A is twice the measure of its complement. What is the measure of A? F 20 H 60 G 30 J 90
11. If m B (180 x) , what is the measure of a supplement of B?
A 180 C (180 x)
B x D (90 x)
12. What is the length of a rectangle if the perimeter is 88 inches and the length is 2 inches more than the width? F 21 in. H 25 in. G 23 in. J 42 in.
13. What is the height of a triangle with an area of 16.5 square meters if the base is 5.5 meters? A 1.5 m C 6 m2 B 3 m D 6 m
14. A circle has an area of 81 square feet. What is its radius? F 9 ft H 20.5 ft G 9 ft2 J 40.5 ft
15. Given GH with endpoints G( 7, 3) and H(7, 11), what are the coordinates of the midpoint of GH ?
A (0, 4) C ( 7, 7)
B (0, 8) D ( 14, 14)
16. M is the midpoint of .RS R has coordinates ( 2, 10), and M has coordinates (3, 5). What are the coordinates of S? F (1, 15) H (8, 0)
G (0.5, 7.5) J (5, 5)
17. What is the distance from M(9, 4) to N( 1, 2)?
A 10 C 2 26
B 10 D 12
18. Given a right triangle with the length of one leg equal to 9 centimeters and the length of the hypotenuse equal to 15 centimeters, what is the length of the other leg?
F 6 cm H 306 cm
G 12 cm J 144 cm
19. What transformation is shown?
A rotation C translation B reflection D image
20. A triangle has vertices A( 3, 6), B(1, 5), and C(2, 4). After a transformation, the image of the triangle has vertices A ( 3, 6), B (1, 5), and C (2, 4). Identify the transformation. F reflection across the x-axis G reflection across the y-axis H rotation J translation
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7.
Name ________________________________________ Date ___________________ Class __________________
11. If B and C are right angles, what additional congruence statement would allow you to prove DCB ABC by the ASA postulate? A DBC ACB B BDC CAB
C AB DC
D AC DB 12. If A and C are right angles and
AD BC , what postulate or theorem justifies the congruence statement BCD DAB?
F SAS H AAS G ASA J HL
13. A right triangle with leg lengths of 4 and 3 units has to be positioned in the coordinate plane to write a coordinate proof. Which set of coordinates would make the proof easier to complete? A (4, 0), (0, 0), (4, 3) B (3, 0), (0, 0), ( 4, 0) C (0, 4), (0, 0), ( 3, 0) D (0, 4), (0, 0), (3, 0)
14. Which of the following would you find most useful in giving a coordinate proof that two triangles are congruent by SSS? F Distance Formula G Midpoint Formula H CPCTC J Slope Formula
15. What is the value of x?
A 12 C 18 B 19.5 D 60
Use the partially completed two-column proof for Exercises 16–18.
Given: GJ bisects FGH, FG HG
Prove: FJ HJ Proof:
16. Which reason belongs in Step 4? F Isosc. Thm. G Conv. of Isosc. Thm. H ASA J Def. of bisector
17. Which reason belongs in Step 5? A Isosc. Thm. C CPCTC B ASA D HL
18. Which reason belongs in Step 6? F Isosc. Thm. G ASA H CPCTC J Def. of bisector
Foundations for Geometry Chapter Test Form C continued
12. Find the area of a rectangle with a length of x 3 meters and a width of 2x meters. Express your answer in terms of x.
_________________________________________
13. The area of a triangle is 8.25 square centimeters. If the base of the triangle is 3 centimeters, what is the height?
_________________________________________
14. Find the radius of a circle with a circumference of 100 inches.
_________________________________________
15. Find the coordinates of the midpoint of GH with endpoints G(3a, 3a) and H( a, 7a).
_________________________________________
16. M bisects .RS R has coordinates ( 2, 3), and M has coordinates (1, 0). Find the coordinates of S.
_________________________________________
17. AB has endpoints A( 6, 4) and B( 1, 8). CD has endpoints C(2, 5) and D(14, 0). Determine whether the two segments are congruent.
________________________________________
18. A ladder is leaning against a building. The distance from the building to the bottom of the ladder is 7 feet. The ladder is 25 feet long. How high up the building is the top of the ladder?
________________________________________
19. Identify the transformation.
________________________________________
20. A transformation maps E onto F and G onto H. Identify the preimage of H.
________________________________________
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9. WXYZ is a rhombus. What is m∠XYZ and
m∠YZW
10.
Name ________________________________________ Date ___________________ Class __________________
Parallel and Perpendicular Lines Chapter Test Form C continued
10. If a transversal is perpendicular to one of two parallel lines, which statement is NOT correct? F All the angles formed are congruent. G Every pair of angles is supplementary. H The transversal is to the other line. J Every pair of angles is complementary.
11. Which is a possible value of x?
A 21 C 25 B 23 D 26
Use the figure and the partially completed proof for Exercises 12 and 13.
Given: AC is the shortest segment from A to CD and m 1 m 2.
Prove: HJJG HJJGAB AC
Proof: Statements Reasons
1. m 1 m 2 1. Given
2. ___?___ 2. Given
3. AC CDHJJG HJJG
3. Distance from a point to a line
4. ? 4. Conv. of Alternate
Int. s/ Thm.
5. HJJG HJJGAB AC 5. ?
12. Which is the statement for Step 2?
F ||HJJG HJJGAB CD H
HJJG HJJGAC CD
G HJJG HJJGBD CD J Not here
13. Which is the justification for Step 5? A 2 lines to same line 2 lines B 2 intersecting lines form linear pair of
lines C Transv. Thm. D Same-Side Interior Angles Theorem
14. Given the point J( 2, 4), for which point K is
HJJGJK a line with undefined slope?
F K(2, 4) H K(4, 2) G K(2, 4) J K( 2, 4)
15. If EF GH for the points E( 2, 5), F(x, y), G( 2, 2), and H(0, 0), which is a possible ordered pair for F? A (2, 1) C (3, 1) B ( 1, 4) D (3, 10)
16. Given points A( 1, 4), B(0, 4), C(2, 0), and D(2, 5), what type of lines are
HJJGAB
and HJJGCD ?
F parallel H horizontal G perpendicular J vertical
17. Which is an equation of a horizontal line? A x 3 C y x B y 4 D y x
18. Which is the equation of a line that does NOT go through the origin? F x 0 H y x G y x 1 J y 2x
19. Which line is NOT parallel to y x2 23
?
A 2x 3y 6 C 6y 12 4x
B y x1 1 12 3
D 4x 6y 12
20. Which of the following is the equation of the line that passes through (2, 1) and is perpendicular to 5x y 9? F x 5y 3 H x 5y 3
Circle the best answer. 1. Which ratio is the slope of the line?
A 13
B 31
2. What is the value of x?
23 12
x
A 8 B 18
3. If 4x 3y, which shows the ratio of x to y in simplest form?
A 43
B 34
4. A student made a model of a building. The model was 3 feet high and 12 feet wide. The building is 720 feet wide. Which proportion correctly shows how to find the height of the building?
A 3 12720 x
B 12 3 720
x
C 312 720
x
5. Which similarity statement is true for the triangles shown?
A UABC UDEF B UABC UFED
6. Which value of x make the two rectangles similar?
A 42 B 63 C 84
7. Which similarity postulate or theorem lets you conclude that UJKL UMNO?
13. Baldwin St. in Duendin, New Zealand, is the steepest street in the world. It has a grade of 38%. To the nearest degree, what angle does Baldwin St. make with the horizontal line? 14. A ramp has a 7% grade. The ramp is 42 ft. long. Find the vertical distance that the ramp rises. Round your answer to the nearest hundredths. 15.A highway exit ramp has a slope of 3/20. To the nearest degree, find the angle that the ramp makes with a horizontal line. 16.
Name ________________________________________ Date ___________________ Class __________________
Choose the best answer. 1. What is the perimeter of this rectangle?
A (4x 3) units C (8x 6) units B (4x 34) units
2. To the nearest whole number, what is the area of this circle? Use the A r2.
F 452 in2 H 38 in2 G 113 in2
3. To the nearest tenth, what is the circumference of a circle with a radius of 4 meters? Use C 2 r. A 50.2 m C 12.6 m B 25.1 m
4. Find the coordinates for the midpoint of MN if M( 3, 8) and N( 7, 6). F ( 5, 7) H (2, 1) G (5, 7)
5. K is the midpoint of PQ , P ( 9, 4), and K ( 1, 6). What are the coordinates of Q? A (5, 10) C (7, 16) B ( 11, 8)
6. What is the distance, to the nearest whole number, from K(5, 6) to P(1, 4)?
Use 2 22 1 2 1( ) ( )d x x y y .
F 13 G 11 H 6
7. Which best describes the transformation?
A reflection (flip) B rotation (turn) C translation (slide)
8. A figure has vertices at K(5, 5), L(5, 3), M(1, 1). After a transformation, the image of the figure has vertices at K'( 5, 5), L'( 3, 5), and M'( 1, 1). Which best describes the transformation? F reflection (flip) G rotation (turn) H translation (slide)
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Name ________________________________________ Date ___________________ Class __________________
Foundations for Geometry Chapter Test Form A continued
11. If m B x , what is the measure of a supplement of B? A 90 C (90 x) B 180 D (180 x)
12. What is the perimeter of a square with s 8 centimeters? A 32 cm B 64 cm
13. What is the area of a triangle with a base of 6 inches and a height of 3 inches? A 9 in2 B 18 in2
14. What is the approximate area of a circle with a radius of 4 feet? Use 3.14 for . A 12.56 ft2 C 50.24 ft2 B 25.12 ft2 D 200.96 ft2
15. What are the coordinates of the midpoint of GH with endpoints G( 2, 5) and H(4, 1)? A ( 6, 4) C ( 3, 2) B (1, 3) D (2, 6)
16. M is the midpoint of RS and R has coordinates (2, 5). M has coordinates (6, 9). Find the coordinates of S. A (4.5, 6.5) C (4, 4) B (10, 13) D (16, 16)
17. Use the Distance Formula to find VW.
A 5 C 9
B 29 D 25
18. Use the Pythagorean Theorem to find the length of the hypotenuse.
A 10 C 48 B 14 D 100
19. What transformation is shown?
A translation B reflection
20. What rule would you use to translate a figure in the coordinate plane 2 units to the right? A (x, y) (x 2, y) B (x, y) (x, y 2)
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18. Which angle has a cosine of 3
5?
A ∠A B ∠B
19. Find sin B and cos A as a fraction. What conclusion can you make about angle A and B?
20. a) Are triangles A(1, 7), B(2, 8), C(3, 7) and D(2.5, 17.5), E(5, 20), F(7.5, 17.5) congruent? Describe the transformation that supports your answer. b) Prove that triangles F(4, 6), G(5, 7),H(7, 4) and J(1, -4), K(2, -5), L(4, -2) are congruent, using transformation, and describe the transformation to support your answer 21.
Name ________________________________________ Date ___________________ Class __________________
Foundations for Geometry Chapter Test Form A continued
Use the figures for Exercises 12–14.
12. Find the perimeter of the square.
_________________________________________
13. Find the area of the triangle.
_________________________________________
14. Find the circumference of the circle. Express your answer in terms of .
_________________________________________
15. Find the coordinates of the midpoint of GH with endpoints G( 5, 4) and H( 5, 8).
_________________________________________
16. M is the midpoint of ,RS and M has coordinates (2, 6). R has coordinates ( 10, 6). Find the coordinates of S.
_________________________________________
17. Use the Distance Formula to find VW.
2 22 1 2 1( ) ( )d x x y y
________________________________________
18. Use the Pythagorean Theorem to find the length of the hypotenuse.
a2 b2 c2
________________________________________
19. Identify the transformation as a reflection, a rotation, or a translation.
________________________________________
20. The coordinates of the endpoints of a segment are A( 2, 3) and B(2, 1). Find the coordinates for the endpoints of the image of AB after the translation (x, y) (x 3, y 2).
________________________________________
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Name ________________________________________ Date ___________________ Class __________________
Foundations for Geometry Chapter Test Form B continued
14. Find the circumference of a circle with a diameter of 6 feet. Use 3.14 for .
_________________________________________
15. Find the coordinates of the midpoint of GH with endpoints G( 7, 3) and H(5, 9).
_________________________________________
16. M is the midpoint of ,RS and M has coordinates ( 1, 5). R has coordinates ( 5, 2). Find the coordinates of S.
_________________________________________
17. Use the Distance Formula to find AB.
_________________________________________
18. Use the Pythagorean Theorem to find VW.
________________________________________
19. Identify the transformation.
________________________________________
20. A triangle has vertices at A( 2, 3), B(2, 1), and C(1, 0). After a transformation, the image of the triangle has vertices at A ( 2, 3), B (2, 5), and C (1, 6). Identify the transformation.
________________________________________
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23.
Name ________________________________________ Date ___________________ Class __________________
25. a) Given the points A(–1, 2) and B(7, 8), find the coordinates of the point P on directed line segment that partitions in the ratio . Plot P. COORD::
b). TWO:: Find the coordinates of P so that P partitions the segment in the ratio 5:1 if A(2, 4) and B(8, 10). (Sketch this on your own) 26.
Name ________________________________________ Date ___________________ Class __________________
Circle the best answer. 1. Which similarity statement is true for
rectangles JKLM and PQRS, given that JK 6, JM 5, QR 15, and PQ 12.5?
A rectangle JKLM rectangle PQRS B rectangle JKLM rectangle QRSP C rectangle JKLM rectangle RQPS D rectangle JKLM rectangle SRQP
2. JKL MNO. The similarity ratio of
JKL to MNO is 52
. What is the length
of MN ?
F 6 G 10.8 H 14 J 37.5
3. An atrium has the dimensions shown. A scale drawing of the atrium is actually 6 cm wide. What is the length of the scale drawing?
A 1.9 cm C 19.2 cm B 3.3 cm D 48 cm
4. Which of the following transformations is NOT a similarity transformation? F M: (x, y) (0.3x, 0.3y) G M: (x, y) (10x, 10y) H M: (x, y) (4x, 2y) J M: (x, y) (0.8x, 0.8y)
been applied to the polygon S(12, 16), T(–12, –16), U(4, 4). What are the coordinates of the image points? A S'(9, 12), T'( 9 , 12), U'(3, 3) B S'(36, 48), T'( 36, 48), U'(12, 12) C S'(12, 16), T'( 12, 16), U'(4, 4)
D S'(12 3 ,4
16 34
), T'( 11 1 ,4
15 14
),
U'(4 3 ,4
4 34
)
6. Polygon K(1, 0), L(8, 3), M(9, 4), N(2, 1) was mapped to polygon O( 1, 1), P(20, 10), Q(23, 13), R(2, 4). What was the similarity transformation? F translate: (x, y) (x 2, y + 1) G first dilate: (x, y) (3x, 3y) then
translate: (x, y) (x – 4, y + 1) H first translate: (x, y) (x – 3, y + 2)
then dilate: (x, y) (0.5x, 0.5y) J translate: (x, y) (x + 0, y + 3)
7. Which similarity postulate or theorem lets you conclude that ABC CDE?
A AA B SAS C SSS D Triangles not similar
Name ________________________________________ Date ___________________ Class __________________
11. If you are using indirect measurement, what is true?
A You must convert dimensions to the same unit of measurement.
B You do not have to convert dimensions to the same unit of measurement.
12. The scale on a map is 1.5 cm : 1280 m. If the distance between the school and the library on the map is 12 centimeters, what is the actual distance between the buildings?
A 15 m
B 150 m
C 9600 m
D 10,240 m
13. Which coordinates for V make SOT UOV?
A (0, 6)
B (4, 0)
C (6, 0)
D (8, 0)
14. ABC has vertices A(0, 0), B(0, 6), and C(4, 0). Which set of coordinates can be used to prove ABC DEF?
Circle the best answer. 1. Which similarity statement appears to be
true for the figures shown?
A pentagon AEDCB pentagon NMLKJ B hexagon DCBAE hexagon MLKJN C pentagon DCBAE pentagon KJMNL D pentagon DCBAE pentagon MLKJN
2. What is CD if .ABCD . ?TUVW
F 12 H 42 G 28 J 84
3. A scale drawing of a specialized boxing ring has the dimensions shown. The actual ring has the dimension shown. What is the value of x?
A 0.625 ft C 8.1 ft B 1.6 ft D 10 ft
4. Which of the following transformations is NOT a similarity transformation? F M: (x, y) (3x, 4y) G M: (x, y) (5x, 5y) H M: (x, y) (0.01x, 0.01y) J M: (x, y) (0.66x, 0.66y)
been applied to the polygon V(–6, 4), W(6 , 8), X(–2, –1). What are the coordinates of the image points? A V (60, –40), W (–60, –80),
X (20, 10) B V (–60, 40), W (60, 80),
X (–20, –10) C V (0.6, –0.4), W (–0.6, –0.8),
X (0.2, 0.1) D V (–0.6, 0.4), W (0.6, 0.8),
X (–0.2, –0.1)
6. Polygon S(10, –4), T(–8, 4), U(5, 5), V(8,0) was mapped to polygon W(6, –3.5) X(–3, 0.5), Y(3.5, 1), Z(5, –1.5). What was the similarity transformation? F translate: (x, y) (x – 4, y – 0.5) G translate: (x, y) (x – 3, y – 1.5) H first translate: (x, y) (x 2, y – 3)
then dilate: (x, y) (0.5x, 0.5y) J first dilate: (x, y) (2x, 2y) then
translate: (x, y) (x – 14, y 4.5)
7. Given EK 29
EG and EJ 29
EF, which
similarity postulate or theorem proves EFG EJK?
A AA B SSS C SAS D Not here
Name ________________________________________ Date ___________________ Class __________________
A XB 20, BY 25 B XB 24, BY 30 C XB 25, BY 20 D XB 32, BY 40
10. In JKL, the bisector of J divides intoKL XK with length y 3 and XL
with length 2y. If JK 12 and JL 16, which could be the length of XK ? F 6 G 9 H 12 J 16
11. A student who is 60 inches tall measured shadows to find the height of a tree. The student’s shadow was 24 inches long, and the shadow of the tree was 13 feet long. Which proportion should the student use to find the height of the tree in inches?
A 60 24156 x
C 6024 13
x
B 5 213 x
D 6024 156
x
12. A blueprint uses a scale of 1.5 in : 24 ft. If the actual room has a width of 12 yards and a length of 17 yards, how long is the room on the blueprint?
F 34
in.
G 1 116
in.
H 2 14
in.
J 3 316
in.
13. Which are the coordinates of ABC with vertices A(0, 2), B( 2, 2), and C(2, 4)
after a dilation with a scale factor of 32
?
A A (0, 3), B ( 3, 3), and C (3, 6) B A (0, 1.6), B ( 1.6, 1.6), and
C (1.6, 4.8) C A (0, 3), B (3, 3), and C (3, 6) D A (1.5, 3), B ( 3, 3), and C (3, 6)
14. STU has vertices S(1, 2), T(2, 4), and U(6, 2). Which set of coordinates can be used to prove PQR STU? F P(0.5, 1), Q(3, 1), and R(1, 2) G P(1.5, 3), Q(3, 6), and R(9, 1.5) H P(1.5, 3), Q(3, 6), and R(3, 1) J P(2, 4), Q(4, 8), and R(12, 4)
Circle the best answer. 1. Which similarity statement is true for
rectangles JKLM and PQRS, given that JK 6, JM 5, QR 15, and PQ 12.5?
A rectangle JKLM rectangle PQRS B rectangle JKLM rectangle QRSP C rectangle JKLM rectangle RQPS D rectangle JKLM rectangle SRQP
2. JKL MNO. The similarity ratio of
JKL to MNO is 52
. What is the length
of MN ?
F 6 G 10.8 H 14 J 37.5
3. An atrium has the dimensions shown. A scale drawing of the atrium is actually 6 cm wide. What is the length of the scale drawing?
A 1.9 cm C 19.2 cm B 3.3 cm D 48 cm
4. Which of the following transformations is NOT a similarity transformation? F M: (x, y) (0.3x, 0.3y) G M: (x, y) (10x, 10y) H M: (x, y) (4x, 2y) J M: (x, y) (0.8x, 0.8y)
been applied to the polygon S(12, 16), T(–12, –16), U(4, 4). What are the coordinates of the image points? A S'(9, 12), T'( 9 , 12), U'(3, 3) B S'(36, 48), T'( 36, 48), U'(12, 12) C S'(12, 16), T'( 12, 16), U'(4, 4)
D S'(12 3 ,4
16 34
), T'( 11 1 ,4
15 14
),
U'(4 3 ,4
4 34
)
6. Polygon K(1, 0), L(8, 3), M(9, 4), N(2, 1) was mapped to polygon O( 1, 1), P(20, 10), Q(23, 13), R(2, 4). What was the similarity transformation? F translate: (x, y) (x 2, y + 1) G first dilate: (x, y) (3x, 3y) then
translate: (x, y) (x – 4, y + 1) H first translate: (x, y) (x – 3, y + 2)
then dilate: (x, y) (0.5x, 0.5y) J translate: (x, y) (x + 0, y + 3)
7. Which similarity postulate or theorem lets you conclude that ABC CDE?
A AA B SAS C SSS D Triangles not similar
Name ________________________________________ Date ___________________ Class __________________
11. If you are using indirect measurement, what is true?
A You must convert dimensions to the same unit of measurement.
B You do not have to convert dimensions to the same unit of measurement.
12. The scale on a map is 1.5 cm : 1280 m. If the distance between the school and the library on the map is 12 centimeters, what is the actual distance between the buildings?
A 15 m
B 150 m
C 9600 m
D 10,240 m
13. Which coordinates for V make SOT UOV?
A (0, 6)
B (4, 0)
C (6, 0)
D (8, 0)
14. ABC has vertices A(0, 0), B(0, 6), and C(4, 0). Which set of coordinates can be used to prove ABC DEF?
Polygons and Quadrilaterals Chapter Test Form C continued
10. Find the perimeter of a square if half of a diagonal is equal to 8 inches.
_________________________________________
11. Determine the value of x.
_________________________________________
12. Write True or False. If the midpoints of the sides of a parallelogram, when connected in order, form a rectangle, then the parallelogram is a rhombus.
_________________________________________
13. Use the diagonals to determine whether a parallelogram with vertices ( 3, 2), ( 1, 4), (8, 5), and (6, 7) is a rectangle, rhombus, or square.
_________________________________________
14. Give the best name for the quadrilateral with vertices ( 1, 1), (1, 3), (3, 1), and (1, 3).
________________________________________
15. Find the value of x so that ABCD is an isosceles trapezoid with bases AD and BC .
________________________________________
16. XY is the midsegment of the trapezoid. Find the value of x.
Properties and Attributes of Triangles Chapter Test Form C
Circle the best answer. 1. AC is the perpendicular bisector of .BD
What is the value of x?
A 2.4 C 263
B 4 D Not here
2. Which is the equation of the line that is the perpendicular bisector of the segment with endpoints (n, 5) and (n, 3)? F y 1 H x 4 G y 4 J y n
3. What is m XYZ?
A 70 C 145 B 125 D Not here
4. Which is the center of the circumscribed circle for the triangle with vertices at (0, 0), (0, 8), and (8, 4)? F (3, 4) H (4, 6) G (4, 3) J (8, 4)
5. Which is the radius of a circle inscribed in KLM?
A the distance from the incenter to a side of the triangle
B the distance from the circumcenter to a side of the triangle
C the distance from the incenter to a vertex of the triangle
D the distance from the circumcenter to a vertex of the triangle
6. If (2, 4) is the location of the centroid of a triangle, which CANNOT be the coordinates of the vertices of the triangle? F (0, 0), (0, 6), (6, 6) G (3, 4), (3, 2), (0, 6) H (3, 2), (1, 6), (2, 8) J (2, 0), (1, 8), (3, 4)
7. Which are the coordinates of the vertices of a triangle with orthocenter ( 4, 3)? A (4, 1), ( 2, 5), (6, 5) B ( 1, 0), ( 1, 5), ( 5, 3) C ( 2, 0), ( 2, 5), ( 5, 3) D ( 4, 0), ( 1, 5), ( 5, 5)
8. ABC is the midsegment triangle of TUV. Which measure CANNOT be
determined?
F m VAC H m CBT G m TAC J m AVC
9. PQ is the midsegment of GHK, and GH is the midsegment of KLM. What is the length of PK ?
A 4 C 14 B 7 D 28
Name ________________________________________ Date ___________________ Class __________________
Properties and Attributes of Triangles Chapter Test Form B continued
9. TUV is the midsegment triangle of ABC. Which angle does NOT
necessarily measure 40 ?
A VTU C CTV B TUA D VBU
10. Which statement is used in an indirect proof to show that an equiangular triangle cannot have a right angle? F Isosc. Thm. G Sum Thm. H Rt. Thm. J Acute of a rt. are
complementary.
11. The lengths of two sides of a triangle are 7 and 11. Which could NOT be the length of the third side? A 5 C 12 B 10 D 19
12. Which statement is false?
F KLM is scalene. G ML KM KL H m L m K J KM ML
13. Which best describes the range of values for x?
A 0 x 7 C x 15 B 0 x 15 D 6 x 7
14. What is the value of x in simplest radical form?
F 3 12 H 72
G 6 2 J 89
15. Which numbers form a Pythagorean triple?
A 3, 4, 6 C 9, 12, 15
B 7, 6 2, 11 D 8, 15, 18
16. Which side length will form an obtuse triangle with sides of length 8 and 10?
F 6 H 12
G 9 J 13
17. What is the value of x in simplest radical form?
10. Which postulate or theorem can you use to prove ABE CDE? A SSS B SAS C ASA D AAS
11. What additional information will prove ABE CDE by HL?
A AB CD
B AE CE
12. To write a coordinate proof, you position a right isosceles triangle in the coordinate plane. The legs measure two units. What is the best position for the vertex angle? A (0,0) B (0,2) C (2, 0) D (2, 2)
13. Given: ABCD is a square with vertices A(0,0), B(0, 4), C(4, 4), and D(4,0). In a coordinate proof, what information would be used to prove AB CD if you do NOT use the distance formula? A x-coordinate of A, x-coordinate of C B y-coordinate of A, y-coordinate of C C y-coordinate of A, x-coordinate of C D x-coordinate of A, y-coordinate of C
14. What is the value of x?
A 22.5 B 30 C 45 D 60
Use the figure for Exercises 15 and 16.
15. What postulate or theorem proves ?HG FG
A Isosceles Triangle Theorem B Converse of Isosceles Triangle
Theorem
16. If FGJ HGJ, what reason justifies the statement HGJ FGJ? A ASA B Reflex. Prop. of C Def. of bisects D CPCTC
Choose the best answer. 1. Which MUST be a square?
A
C
B
D
2. Which is NOT necessarily a rhombus?
F H
G J
3. PQRS is a rectangle. Find ST.
A 10 C 12.5 B 12 D 25
4. Quadrilateral RSTU is a parallelogram. What other information would allow you to prove that RSTU is a rectangle? F Opposite angles are congruent. G Opposite sides are congruent. H The diagonals bisect the angles. J The diagonals are congruent.
5. WXYZ is a rhombus. What is m XYZ?
A 100 C 140 B 120 D 160
6. KLMN is a square and LN NP .
Which can be proved? F KPN KQN
G ||PN KM
H KQ PN
J KP 12
LN
7. A certain kite has exactly one acute angle, and it measures 16 . What is the maximum whole-number measure of the angle opposite that angle? A 74 C 106 B 90 D 164
8. Three sides of a kite measure 8 inches, 10 inches, and 8 inches. What is the perimeter of the kite? F 26 in. H 34 in. G 28 in. J 36 in.
9. A trapezoid midsegment measures 6. One of the bases measures 10. What is the measure of the other base? A 2 C 14 B 8 D 16