Geometry Semester 1 Name

1

Geometry Semester 1 Name: _____________________________

Final Exam Review Date: __________ Period: __________

Formulas: Definitions:

1. Slope - 1. Complementary –

2. Midpoint - 2. Supplementary –

3. Bisect –

3. Distance - 4. Vertical Angles –

4. Pythagorean Theorem – 5. Perpendicular –

5. Point – slope Form –

6. Slope – Intercept Form – Triangle Congruence Criterion:

Transformations:

1. Translation – Triangle Similarity Criterion:

2. Reflections –

3. Rotations – Type of Sentences:

a. 𝑅𝑜, 90° 1. Conditional –

b. 𝑅𝑜,−90° a. Hypothesis –

c. 𝑅𝑜,180° b. Conclusion –

4. Rotational Symmetry – 2. Converse –

3. Inverse –

4. Contrapositive –

5. Conjecture –

6. Bi – Conditional –

Theorems:

• All radii of a circle are congruent

• If two lines are parallel, then their slopes are equal

• If two lines are perpendicular each line’s slope is the opposite reciprocal of the other’s

• The sum of the measures of the angles in a triangle is 180 degrees

• The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote

interior angles

• A segment joining the midpoints of two sides a of a triangle is parallel to the 3rd side, and its

length is one half the length of the 3rd side (Triangle Midsegment Theorem)

• The median of a trapezoid is parallel to the bases and its length is the average of the lengths of the

base. (Trapezoid Median Theorem)

2

Properties and Definitions

Quadrilaterals:

Parallelogram: Kite:

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Rectangle: Trapezoid:

1.

2.

• Plus all 5 properties of the Parallelogram

Isosceles Trapezoid:

Rhombus: 1.

1. 2.

2.

3.

• Plus all 5 properties of the Parallelogram

Square: Ways to prove Quad. is a parallelogram

•All 5 properties of the Parallelogram 1.

• 2 properties of the Rectangle 2.

• 3 properties of the Rhombus 3.

4.

5.

3

Q

P

R

U

T

S

Geometry Semester 1 Name: _____________________________

Final Exam Review Date: ____________ Period: __________

UNIT 1 – ACTIVITIES 1 – 8

1. Identify the following on the given picture:

a. Chord:

b. Diameter:

c. Radius:

d. Center:

2. Given Circle P.

a. Put the following segments in order from smallest to largest:

𝐴𝐵̅̅ ̅̅ , 𝐷𝐵̅̅ ̅̅ , 𝑃𝐶̅̅̅̅

b. If AC = 12, find PD.

3. Write all possible names for ∠2?

__________ 4. Suppose point D is in the interior ∠𝐴𝐵𝐶, 𝑚∠𝐴𝐵𝐶 = 12𝑥 − 110, 𝑚∠𝐴𝐵𝐷 = 3𝑥 + 40, and

𝑚∠𝐷𝐵𝐶 = 2𝑥 − 10. What is 𝑚∠𝐴𝐵𝐶?

5. Which angle pairs in the figure are adjacent and supplementary? Check all that apply.

_______ ∠𝐷𝐵𝐶 and ∠𝐶𝐵𝐸

_______ ∠𝐴𝐵𝐷 and ∠𝐶𝐵𝐸

_______ ∠𝐴𝐵𝐹 and ∠𝐹𝐵𝐸

_______ ∠𝐴𝐵𝐷 and ∠𝐷𝐵𝐶

_______ ∠𝐶𝐵𝐸 and ∠𝐸𝐵𝐴

A

D

B C

F E

A

B C

D

2 1

A

D P

B

C

4

__________ 6. In the diagram shown, AB ⊥ PQ. If PT = TQ, which statement is true?

A. AT = TB

B. 𝑃𝑄̅̅ ̅̅ is the perpendicular bisector of 𝐴𝐵̅̅ ̅̅

C. 𝐴𝐵̅̅ ̅̅ is the perpendicular bisector of 𝑃𝑄̅̅ ̅̅

D. 𝑃𝑇̅̅̅̅ is the perpendicular bisector of 𝐴𝐵̅̅ ̅̅

__________ 7. Find the measure of 1m .

__________ 8. Alison states ∠𝐴𝑀𝐶 + ∠𝐶𝑀𝐷 + ∠𝐷𝑀𝐵 = ∠𝐴𝑀𝐵. Which justifies Alison’s statement?

A. Angle Addition Postulate

B. Segment Addition Postulate

C. Construction of an Angle Bisector

D. Construction of a Perpendicular Bisector

__________ 9. Suppose 𝑄 is the midpoint of 𝑃𝑅̅̅ ̅̅ , 𝑃𝑄 = 𝑥 + 10, and 𝑄𝑅 = 4𝑥 − 2. What is the value of 𝑃𝑅

__________ 10. If ∠𝐷 and ∠𝐶 are complementary, 𝑚∠𝐶 = 3x and 𝑚∠𝐷 = 4x + 6, find 𝑚∠𝐶.

__________ 11. For 𝐴𝐵̅̅ ̅̅ , point A has coordinates (3, -5) and point B has coordinates (-1, 9). What are the

coordinates of the midpoint of 𝐴𝐵̅̅ ̅̅ ?

__________ 12. Julie is given two points, A(5, 4) and B(3, -2). Find AB.

P

Q

T

B

A

1 ° °

5

p

n

m

8 7 6 5

4 3

2 1

__________ 13. Name each angle pair in the given diagram.

A. ∠2 and ∠6

B. ∠8 and ∠5

C. ∠4 and ∠5

D. ∠4 and ∠6

__________ 14. Billy is working on a proof given 𝑥 ∥ 𝑡 and 𝑘 ∥ 𝑤 as shown. He wants to write a statement that

can be justified using only the Corresponding Angles Postulate. Which statement could he write?

A. ∠2 and ∠4

B. ∠2 and ∠6

C. ∠2 and ∠8

D. ∠2 and ∠10

__________ 15. Use the diagram from #14. Given 𝑥 ∥ 𝑡 and 𝑘 ∥ 𝑤 if 𝑚∠12 = 110°, find 𝑚∠3.

__________ 16. How could you justify that ∆𝐴𝐵𝐶 is a right triangle?

A. The slope of 𝐵𝐶̅̅ ̅̅ = −2

1 and the slope of 𝐵𝐴̅̅ ̅̅ = −

1

3

B. The slope of 𝐶𝐴̅̅ ̅̅ =1

2 and the slope of 𝐵𝐴̅̅ ̅̅ = −

1

3

C. The slope of 𝐵𝐶̅̅ ̅̅ = −2

1 and the slope of 𝐶𝐴̅̅ ̅̅ =

1

2

D. The slope of 𝐵𝐶̅̅ ̅̅ = −2

1 and the slope of 𝐵𝐴̅̅ ̅̅ = −

1

3

A( 3, 1 )

B( -6, 4 )

C( -3, -2 )

16

9 10 11

12

13 14

15

7 6 5

4 3 2 1

t x

k

w 8

6

17. What is the equation of the line parallel to the line 5𝑦 + 2𝑥 = −25 and passes through the point (5, −3).

18. Write the equation of the line that is parallel to the line 𝑦 = −2𝑥 + 3 and passes through the point ( -7, 9 ).

19. Write the equation of the line perpendicular to the line 𝑥 + 𝑦 = 2 and passes through the point ( -5, 8 ).

20. What is the equation that represents a line perpendicular to the line shown on the graph through

the same y-intercept?

21. Circle the hypothesis of the conditional statement below and underline the conclusion.

Conditional: If it is snowing, then we will make a snowman.

( -3, 3 )

( 3, -1 )

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__________ 22. Consider the conditional statement shown.

If a student plays the trumpet, then the student is in the school band.

Which is a counterexample to this conditional statement?

A. A student can be in the band but not play the trumpet

B. A student may not be in the band and not play the trumpet

C. A student can play the trumpet but not be in the school band

D. A student may not play the trumpet but still be in the school band

__________ 23. The distance between two points on a number line is 8 units. Point A is at 6. What are

possible location(s) for point B.

UNIT 2 – ACTIVITIES 9 – 16

24. Consider the arrows on the coordinate grid. Name a transformation that shows the figures are congruent.

25. Complete the table using the translation of a rectangle (x, y) → (x - 1, y + 3).

Point Preimage Image

A (2,-1)

B (2, -3)

C (6,-1)

D (6,-3)

26. Regular polygons have rotational symmetry with angles of rotation listed below. Name each polygon.

a. 36°

b. 60°

8

27. Complete the table below by listing the image vertices after a transformation 𝑟𝑦=0 .

28. The band is practicing a new rigid transformation halftime routine. What happens to the distance between

each band member as they move?

29. Describe each mapping as a single transformation:

a. Figure 1 Figure 3 b. ∆𝑂𝑀𝑁 ∆𝐵𝐴𝐶

30. Describe the translation using

coordinate notation.

31. Suppose ∆𝑄𝑅𝑆 and ∆𝑇𝑈𝑉 are congruent right triangles such that ∠𝑅 is a right angle and ∠𝑉 = 35°

𝑎𝑛𝑑 ∠𝑇 = 5𝑥. Solve for x.

Point Preimage Image

A (2,-1)

B (2, -3)

C (6,-1)

D (6,-3)

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32. Given the information provided, name the method, if any, that can be used to prove the triangles congruent:

33. What additional information need to be given to develop the proof that LHJFHN by ASA

congruence criteria?

34. What additional information need to be given to develop the proof that CDBABD by SAS

congruence criteria?

35. What additional information need to be given to develop the proof that EMREMH by HL

congruence criteria?

36. Which statement could be used in a proof with the reason CPCTC after proving ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐹𝐺?

Circle all that apply.

A. 𝐴𝐶̅̅ ̅̅ ≅ 𝐸𝐺̅̅ ̅̅

B. 𝐴𝐵̅̅ ̅̅ ∥ 𝐸𝐹̅̅ ̅̅

C. 𝐵𝐶̅̅ ̅̅ ≅ 𝐹𝐺̅̅ ̅̅

D. ∠𝐵𝐶𝐴 ≅ ∠𝐹𝐺𝐸

E. ∠𝐶𝐵𝐴 ≅ ∠𝐺𝐸𝐹

37. What are the ways to prove two triangles are congruent?

H J

F

N L

A

D

C

B

E

M R H

10

__________38. Given two triangles with the properties shown.

What additional information needs to be marked to develop the proof that ∆𝐴𝐵𝐶 ≅ ∆𝐴𝐷𝐶 by

the ASA congruence criteria?

A. ∠1 ≅ ∠2 and ∠𝐵 ≅ ∠𝐷

B. 𝐴𝐵̅̅ ̅̅ ≅ 𝐵𝐶̅̅ ̅̅ and 𝐴𝐷̅̅ ̅̅ ≅ 𝐶𝐷̅̅ ̅̅

C. ∠1 ≅ ∠2 and ∠𝐵𝐴𝐶 ≅ ∠𝐷𝐴𝐶

D. 𝐶𝐷̅̅ ̅̅ ≅ 𝐵𝐶̅̅ ̅̅ and 𝐴𝐵̅̅ ̅̅ ≅ 𝐴𝐷̅̅ ̅̅

__________39. RST has angle measures given by 299 += xRm , xSm 593 −= , and 210 += xTm .

What is the measure of T ?

__________40. Find m∠𝑉.

41. Write a two-column proof.

A

D

C

B

2 1

11

Congruence is

reflexive

42. Using the flowchart proof, FILL IN THE BLANKS on the corresponding two-column proof.

Given: Isosceles ∆𝐹𝐺𝐻 with base 𝐺𝐻̅̅ ̅̅ and median 𝐸𝐹̅̅ ̅̅ .

Prove: ∆𝐺𝐹𝐸 ≅ ∆𝐻𝐹𝐸

Statement Reasons

1. Isosceles FGH with base GH 1. Given

2. 2. Definition of isosceles triangle

3. EF is a median 3. Given

4. 4. Definition of median

5. EFEF 5.

6. HFEGFE 6. SSS Congruence Postulate

43.

44. When can you use CPCTC?

F

G E

H

SSS Congruence

Postulate

Definition of

median

Definition of

Isosceles triangle

Isosceles ∆𝐹𝐺𝐻 with base

𝐺𝐻̅̅ ̅̅ Given

𝐺𝐹̅̅ ̅̅ ≅ 𝐻𝐹̅̅ ̅̅

∆𝐺𝐹𝐸 ≅ ∆𝐻𝐹𝐸 𝐸𝐹̅̅ ̅̅ is a median 𝐺𝐸̅̅ ̅̅ ≅ 𝐻𝐸̅̅ ̅̅

Given

EF̅̅̅̅ ≅ EF̅̅̅̅

12

__________ 45. What values of x and y would prove that PQ is the midsegment of trapezoid JKLM.

__________ 46. Which of the following are sufficient to prove a quadrilateral is a parallelogram?

I. Show both pairs of opposite sides parallel.

II. Show both pairs of opposite angles are congruent.

III. Show both pairs of opposite sides congruent.

IV. Show one pair of opposite sides are both parallel and congruent.

V. Show the diagonals bisect each other.

A. I, II, III only

B. I, II, III, and IV only

C. I, II, III, and V only

D. I, II, III, IV and V

__________ 47. Which statement cannot be used to show that quadrilateral XYZW is a parallelogram?

A. 𝑋𝑌̅̅ ̅̅ ∥ 𝑊𝑍̅̅ ̅̅ ̅ and 𝑌𝑍̅̅̅̅ ∥ 𝑋𝑊̅̅ ̅̅ ̅ B. XW = WZ and XY = YZ

C. ∠𝑊𝑋𝑌 ≅ ∠𝑌𝑍𝑊 and ∠𝑋𝑌𝑍 ≅ ∠𝑍𝑊𝑋

D. 𝑋𝑌̅̅ ̅̅ ≅ 𝑊𝑍̅̅ ̅̅ ̅ and 𝑋𝑊̅̅ ̅̅ ̅ ≅ 𝑌𝑍̅̅̅̅

__________ 48. Given the diagram in #48 is a parallelogram, if 𝑚∠𝑊 = 72°, find the other 3 angle measures.

__________ 49. Which of the following must be a parallelogram? Select all that apply.

a. b. c. d.

__________ 50. Given square QRST, solve for x and y.

J

L

Q

K

x

P

4 y

M

10

X Y

Z W

13

UNIT 3 – ACTIVITIES 17 – 18

51. The original photo of the basketball team is 4 inches by 6 inches. The school wants to enlarge it to display it

in the gym. If the enlargement has a new width of 5 feet, then find the new length.

For questions 53 and 54, use the following diagram.

52. Classify the dilation from ∆𝐴𝐵𝐶 → ∆𝐴’𝐵’𝐶’.

53. State the scale factor from ∆𝐴𝐵𝐶 → ∆𝐴’𝐵’𝐶’.

__________ 54. Ramon places a mirror on the ground 45 ft from the base of a flagpole. He walks backwards

until he can see the top of the flagpole in the middle of the mirror. At that point, Ramon’s

eyes are 6 ft above the ground and he is 7.5 ft from the mirror. What is the height of the

flagpole.

55. Given that the triangles are similar, solve for x.

E

D

C

A

B

A’

B’ C’

6

8

5

B C

36

48

30

A