Geometry Honors Semester 1 Review 2015 - 2016 Revised 2015 Geometry Honors Semester 1 Review Page 1 of 16 A B C 1. Match each vocabulary word to the picture. A. Linear Pair B. Vertical Angles C. Angle Bisector D. Parallel Lines E. Orthocenter F. Centroid 2. Name all the possible segments on . For questions 3 – 4 use the diagram below. 3. Name all possible lines on the given figure. 4. Name all possible rays on the given figure. 5. AC = 72 BC = ______ 6. Solve for x. 7. Find ∠ m CAB ______ 8. AB !" !! bisects CAT ∠ . If 30 m CAT ∠ = and 2 10 m CAB x ∠ = + then give the value of x. 9. AB !" !! bisects CAT ∠ . If 8 30 m CAT x ∠ = − and 2 10 m CAB x ∠ = + then give the value of x. A P1 A B E C D P3 A B E C D P4 P5 P D A B C Z V U X Y W + ° (3 10) x + ° (2 15) x − ° (6 125) x + ° (2 39) x T C B M 2x + 3 5x - 8 A C D P6 B
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24. Which are congruent? (Check ü) A. Base angles of an isosceles triangle __ B. Corresponding angles of parallel lines __ C. Diagonals of a rectangle __ D. Diagonals of an isosceles trapezoid __ E. Vertical angles __ F. Linear pairs __ G. Alternate interior angles of parallel lines__ H. Opposite angles of a parallelogram __ I. Consecutive angles of a parallelogram__
25. Which of the following are supplementary? (Check ü)
A. Base angles of an isosceles triangle __ B. Corresponding angles of parallel lines __ C. Diagonals of a rectangle __ D. Diagonals of an isosceles trapezoid __ E. Vertical angles __ F. Linear pairs __ G. Alternate interior angles of parallel lines__ H. Opposite angles of a parallelogram __ I. Consecutive angles of a parallelogram__
two real numbers a and b, if a < b, then a2 < b2.” Select ALL that can be used to prove that the statement is sometimes false? A. a = -4 and b = 3 B. a = 4 and b = 5 C. a = -6 and b = 4 D. a = -1 and b = 2
27. Fill out the reasons for the algebraic proof: Given: 5(x + 2) – 4 = 21 Prove: x = 3
28. Which is the converse of the statement “If a triangle has all acute angles then it is an acute triangle.”? A. If a triangle has all acute angles, then
it is an acute triangle. B. If a triangle is an acute triangle then it
has all acute angles. C. If a triangle does not have all acute
angles then it is not an acute triangle. D. If a triangle is not an acute triangle
then it does not have all acute angles.
29. Name the corresponding congruent parts of the following triangles.
30. What is the value of y?
31. What is the value of ?
32. 𝐺𝑖𝑣𝑒𝑛 ∠𝑅 ≅ ∠𝑇𝑎𝑛𝑑 ∠𝑅𝑆𝑈 ≅ ∠𝑇𝑈𝑆. We know △ 𝑅𝑈𝑆 ≅ △ 𝑇𝑆𝑈 by ? A. SSS B. SAS C. AAS D. ASA
33. If bisects and 𝐶𝐵 ≅ 𝐷𝐵 then we
can prove △ 𝐴𝐶𝐵 ≅ △ 𝐴𝐷𝐵 by what theorem or postulate?
34. If △ 𝑅𝑈𝑆 ≅ △ 𝑇𝑆𝑈 (not shown) then which is NOT true?
A. RS TU≅ B. ∠𝑆𝑈𝑅 ≅ ∠𝑈𝑆𝑇
C. RU TS≅ D. ∠𝑈𝑆𝑅 ≅ ∠𝑈𝑆𝑇
35. Given ∠𝑅 ≅ ∠𝑇, ∠𝑅𝑆𝑈 ≅ ∠𝑇𝑈𝑆 then △ 𝑅𝑈𝑆 ≅ △ ?
A. SUT B. STU C. TSU D. TUS E. The triangles are not congruent
36. A mobile maker wants to place a weight at the center of gravity of a triangular piece of metal. Which does she need? A. circumcenter B. orthocenter C. incenter D. centroid
37. If F, B and D are midpoints of
EC, AC, and AE respectively, then…
A. What point is G called? _____________
B. True or False: G the center of gravity of the triangle. ____________________
C. If AG = 10 then GF = ___________
D. If DG = 18 then DC = ___________
E. If EB = 21 then GB = ___________
38. If Q is the midpoint of MK and ∠𝐽 ≅ ∠𝐿 then the triangles are congruent by
A. SSS B. SAS C. AAS D. ASA
39. Draw in the lines of symmetry for each of the concave figures above.
For questions 47 - 49 use the diagram below. 𝑁𝐴 bisects GNP∠ 47. GA = 16, AP = 20, NP = 25, GN = ______ 48. GN = 15, NP = 18, GP = 25, GA = _______ 49. GA = 12, AP = 2x + 3, NP = 5 + x, GN = 15 What is the value of x?
A. 56
B. 514
C. 83
D. 8
50. A triangle has sides 12 ft, 14 ft and 20 ft.
The smallest side of another, similar triangle measures 8 ft. What is the perimeter of the smaller triangle?
51. The diagram above may not be drawn
to scale.
If ∆𝑅𝑆𝑇 ~ ∆𝑈𝑃𝑄 then find the value of x. Round to the nearest tenth.
A. 34.5 B. 36.2 C. 11.6 D. 12.2
52. Find the value of x. Round to the tenth
place if needed.
53. In the figures below, ~MAP BOXΔ Δ . If
75m A∠ = ° and 50m X∠ = ° , what is ?m B∠ ?
54. Polygon RVTUS ~ Polygon MNPQR.
SU=10, and side lengths of MNPQR are shown. What is the perimeter of RVTUS?
55. Roger is 6 feet tall and stands by a flag pole. Roger casts a 5 foot shadow at the same time of day that the flag pole casts a 9 foot shadow.
How tall is the flag pole? A. 10.8 ft B. 8 ft C. 10 ft D. 7.5 ft
56. , AE=10, EC=8, AC=9, FD=12. HC=6.
A. What conjecture states is
∆𝐴𝐶𝐸 ~ ∆𝐵𝐷𝐹 ? ________
B. Find BC=____
C. Find BH=____
D. Find HF=_____
57. If angle R is congruent to angle N then RO = _____ and OF = ______
58. Faith, who will play ball on a new type of
field (shown below), will be the pitcher. Faith will stand an equal distance from Marie, Linda and Brenda. At which point should Faith stand in the MBL triangle?
A. Every point in a plane which is on the ________________________ is equidistant from the sides of an angle. B. Every point in a plane which is on the _______________________ is equidistant from the endpoints of a segment. C. The point called the ____________ is equidistant to the sides of the triangle, D. The point called the ____________ is equidistant to the vertices of a triangle.
83. Classify the transformation. (The shaded figure is the pre-mage)
84. In the figure below, the dashed figure is the preimage, and the solid outlined figure is the image. What is the transformation rule of the translation below?
85. Draw a 180o counterclockwise rotation of the figure below and identify the new coordinates of each vertex.
86. Based on the measurements below, does 𝑀𝑇 bisect ∠𝐴𝑀𝐻 ? Why or why not?