Download Math 2 Unit 4 Test _ NS

MATH 2 UNIT 4 TEST
G-CO.9
1. In this figure, lines a, b, c, d, and e intersect as shown.
Note: The figure is not drawn to scale.
Based on the angle measures, which pair of lines is parallel?
a. a and b
b. c and e
c. c and d
d. d and e
G-CO.9
̅̅̅̅ is parallel to 𝐶𝐷
̅̅̅̅.
2. In the figure below, 𝐴𝐵
Which statement proves that ∠3 ≅ ∠7?
a. If two parallel lines are cut by a transversal, the alternate interior angles are congruent.
b. If two parallel lines are cut by a transversal, the alternate exterior angles are congruent.
c. If two parallel lines are cut by a transversal, the corresponding angles are congruent.
d. If two parallel lines are cut by a transversal, the vertical angles are congruent.
G-CO.9
3. In this figure, lines a and b are intersected by line 𝑡.
Which of these statements proves that lines a and b are parallel?
a. ∠1 ≅ ∠2
b. ∠1 ≅ ∠3
c. ∠2 ≅ ∠3 are complimentary
d. ∠1 ≅ ∠2 are supplementary
MATH 2 UNIT 4 TEST
G-CO.9
4. In the diagram below Points G, H, and I are collinear.
Which conjecture is not necessarily true?
a. ∠𝐺𝐻𝐾 ≅ ∠𝐾𝐻𝐼
b. 𝑚∠𝐺𝐻𝐽 + 𝑚∠𝐽𝐻𝐼 = 180°
c. ∠𝐺𝐻𝐽 𝑎𝑛𝑑 ∠𝐽𝐻𝐼 form a linear pair
d. ∠𝐺𝐻𝐾 ≅ ∠𝐽𝐻𝐼 are vertical angles
G-SRT.1b
̅̅̅̅̅̅ is the result of dilating 𝑋𝑌
̅̅̅̅ about the origin.
5. In the grid, 𝑋′𝑌′
What scale factor was used in this dilation?
1
a. 4
1
b. 3
3
c. 4
4
d. 3
MATH 2 UNIT 4 TEST
G-SRT.1b
6. Rectangle QUAD is dilated by a factor of 3, with the origin as the center of the dilation. The dilation
forms rectangle Q’U’A’D’.
What is the length of ̅̅̅̅̅̅
𝑄′𝑈′?
a. 2 units
b. 6 units
c. 9 units
d. 18 units
G-SRT.1c
7. On the coordinate grid below, ∆𝑇𝑉𝑊 𝑎𝑛𝑑 ∆𝑋𝑌𝑍 are shown.
Which statement can be used to prove that ∆𝑇𝑉𝑊 ~ ∆𝑋𝑌𝑍?
a. ∆𝑋𝑌𝑍 is the result of a reflection and dilation of ∆𝑇𝑉𝑊, and all angle measures are preserved with
these transformations.
b. ∆𝑋𝑌𝑍 is the result of a rotation and dilation of ∆𝑇𝑉𝑊, and all angle measures are preserved with
these transformations.
c. ∆𝑋𝑌𝑍 is the result of a translation and rotation of ∆𝑇𝑉𝑊, and all side lengths are preserved within
these transformations.
d. ∆𝑋𝑌𝑍 is the result of a reflection and rotation of ∆𝑇𝑉𝑊
MATH 2 UNIT 4 TEST
G-SRT.1c
8. The dilation centered at O with a scale factor of 3. OA = 6cm, OB = 7cm and AB = 8cm.
What is the length of A’B’?
a. 18 cm
b. 21 cm
c. 24 cm
d. 27 cm
G-SRT.1d.
9. The figure below shows a ∆𝐴𝐵𝐶 and its dilation image ∆𝐷𝐸𝐹.
Which statement must be true?
̅̅̅̅ = ̅̅̅̅
a. 𝑚∠𝐴 = 2𝑚∠𝐷 𝑎𝑛𝑑 2𝐵𝐶
𝐸𝐹
̅̅̅̅ = ̅̅̅̅
b. 𝑚∠𝐵 = 𝑚∠𝐸 𝑎𝑛𝑑 2𝐵𝐶
𝐸𝐹
̅̅̅̅ = ̅̅̅̅
c. 𝑚∠𝐵 = 𝑚∠𝐸 𝑎𝑛𝑑 𝐵𝐶
𝐸𝐹
̅̅̅̅
d. 𝑚∠𝐴 = 2𝑚∠𝐷 𝑎𝑛𝑑 𝐵𝐶 = ̅̅̅̅
𝐸𝐹
G-SRT.1d
10. Mr. Williams drew ∆𝐴𝐵𝐶 on a coordinate grid and asked his students to determine the
transformations that will result in a transformed figure ∆𝐴′𝐵′𝐶′ such that ∆𝐴′𝐵′𝐶′ is similar but NOT
congruent to ∆𝐴𝐵𝐶. Two student responses are show below.
Student 1: Reflect ∆𝐴𝐵𝐶 across the y-axis and then dilate it by a scale factor of 1 with the center
of dilation at the origin.
Student 2: Dilate ∆𝐴𝐵𝐶 by a scale factor of 2 and the center of dilation at the origin and then
reflect it across the axis.
Which statement is true?
a. Neither student 1 nor student 2, because dilations and reflections preserve both side lengths and
angle measures.
b. Both student 1 and student 2, because dilations and reflections preserve angle measures but not side
lengths.
c. Only student 2, because dilations preserve angle measure and side lengths are proportional.
d. Only student 1, because this dilation preserves angle measures and side lengths.
MATH 2 UNIT 4 TEST
G-SRT.2
1
11. If ∆𝐿𝑀𝑁 ~ ∆𝑅𝑆𝑇 and MN = 2 𝑆𝑇, which statement must be true?
a. 𝑅𝑇 = 2𝐿𝑁
1
b. 𝑅𝑆 = 2 𝐿𝑀
c. 𝑚∠𝑆 = 2𝑚∠𝑀
1
d. 𝑚∠𝑇 = 2 𝑚∠𝑁
G-SRT.2
12. Quadrilaterals PQRS, I, II, III and IV are shown on the coordinate grid below.
Which quadrilateral is not similar to PQRS?
a. I
b. II
c. III
d. IV
G-SRT.2
13. Triangle PQR is similar to Triangle WXY.
Which proportion describes the relationship between corresponding sides of the triangles?
𝑄𝑅
6
a. 𝑋𝑌 = 3
𝑃𝑄
2
𝑄𝑅
3
𝑃𝑄
2
b. 𝑊𝑋 = 4
c. 𝑊𝑋 = 4
d. 𝑋𝑌 = 6
MATH 2 UNIT 4 TEST
G-SRT.2
14. Given:
𝐴𝐶
𝐸𝐷
𝐵𝐶
= 𝐹𝐷 𝑎𝑛𝑑 ∠𝐵 ≅ ∠𝐹.
Which statement must be true?
̅̅̅̅ ≅ 𝐷𝐸
̅̅̅̅
a. 𝐴𝐶
̅̅̅̅ ≅ ̅̅̅̅
b. 𝐴𝐵
𝐸𝐹
c. ∆𝐴𝐵𝐶 ~ ∆𝐸𝐹𝐷
d. ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐹𝐷
G-SRT.3
15. In the figure below, ∆𝐴𝐵𝐶 was dilated and then rotated 180° about point C to create ∆𝐸𝐷𝐶, as
shown below.
Based on the given transformations, which relationships must be true?
a. ∠𝐴 ≅ ∠𝐷 𝑎𝑛𝑑 ∠𝐵 ≅ ∠𝐸, 𝑠𝑜 ∆𝐴𝐵𝐶 ~ ∆𝐷𝐸𝐶
b. ∠𝐴 ≅ ∠𝐸 𝑎𝑛𝑑 ∠𝐵 ≅ ∠𝐷, 𝑠𝑜 ∆𝐴𝐵𝐶 ~ ∆𝐷𝐸𝐶
c. ∠𝐵𝐶𝐴 ≅ ∠𝐷𝐶𝐸 𝑎𝑛𝑑 ∠𝐵 ≅ ∠𝐸, 𝑠𝑜 ∆𝐴𝐵𝐶 ~ ∆𝐷𝐸𝐶
d. ∠𝐴𝐶𝐵 ≅ ∠𝐸𝐶𝐷 𝑎𝑛𝑑 ∠𝐴 ≅ ∠𝐷, 𝑠𝑜 ∆𝐴𝐵𝐶 ~ ∆𝐷𝐸𝐶
G-SRT.3
16. Two triangles are shown below.
Based on the graph, which statement appears to be true?
a. ∆𝐴𝐵𝐶 ~∆𝑍𝑋𝑌 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 ∠𝐵 ≅ ∠𝑌 𝑎𝑛𝑑 ∠𝐶 ≅ ∠𝑋
b. ∆𝐴𝐵𝐶 ~∆𝑍𝑌𝑋 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 ∠𝐵 ≅ ∠𝑌 𝑎𝑛𝑑 ∠𝐶 ≅ ∠𝑋
c. ∆𝐴𝐵𝐶 ~∆𝑍𝑋𝑌 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 ∠𝐵 ≅ ∠𝑋 𝑎𝑛𝑑 ∠𝐶 ≅ ∠𝑌
d. ∆𝐴𝐵𝐶 ~∆𝑍𝑌𝑋 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 ∠𝐵 ≅ ∠𝑋 𝑎𝑛𝑑 ∠𝐶 ≅ ∠𝑌
MATH 2 UNIT 4 TEST
G-SRT.4
⃡ , as shown below.
17. Triangle ABC is divided by 𝐷𝐸
⃡ ∥ 𝐷𝐸
⃡ ?
What value of x guarantees that 𝐵𝐶
a. 4
b. 4.5
c. 8
d. 10.5
MATH 2 UNIT 4 TEST
G-SRT.4
18. Jamelia is trying to prove that for the figure below, ̅̅̅̅
𝐷𝐸 ∥ ̅̅̅̅
𝐵𝐶 . She is given the information that
𝐷𝐵
𝐴𝐷
𝐸𝐶
= 𝐴𝐸 and lists the first five statements of her proof.
What are the correct remaining statements in Jamelia’s proof?
a.
6. ∆𝐴𝐷𝐸 ~∆𝐴𝐵𝐶
7. ∠𝐴𝐶𝐵 ≅ ∠𝐴𝐵𝐶
8. ̅̅̅̅
𝐷𝐸 ∥ ̅̅̅̅
𝐵𝐶
b.
6. ∆𝐴𝐷𝐸 ~∆𝐴𝐵𝐶
7. ∠𝐴𝐷𝐸 ≅ ∠𝐴𝐵𝐶
̅̅̅̅
̅̅̅̅ ∥ 𝐵𝐶
8. 𝐷𝐸
c.
6. ∠𝐴 ≅ ∠𝐴
7. ∆𝐴𝐷𝐸 ~∆𝐴𝐵𝐶
8. ∠𝐴𝐶𝐵 ≅ ∠𝐴𝐵𝐶
̅̅̅̅
̅̅̅̅ ∥ 𝐵𝐶
9. 𝐷𝐸
d.
6. ∠𝐴 ≅ ∠𝐴
7. ∆𝐴𝐷𝐸 ~∆𝐴𝐵𝐶
8. ∠𝐴𝐷𝐸 ≅ ∠𝐴𝐵𝐶
̅̅̅̅
̅̅̅̅ ∥ 𝐵𝐶
9. 𝐷𝐸
MATH 2 UNIT 4 TEST
G-SRT.10d
19. In ∆𝐴𝐵𝐶, 𝐴𝐷 = 𝐷𝐵 𝑎𝑛𝑑 𝐴𝐸 = 𝐸𝐶.
Given the information above, which statement can be proved to be true?
a. ∆𝐴𝐵𝐶 is isosceles
b. ̅̅̅̅
𝐷𝐸 ⊥ ̅̅̅̅
𝐴𝐶
c. 𝐷𝐸 =
1
𝐵𝐶
2
d. ∆𝐴𝐵𝐶 ≅ ∆𝐴𝐷𝐶
G-SRT.10d
20. Which of the following facts would be sufficient to prove that triangles ABC and DBE are similar?
a. ̅̅̅̅
𝐶𝐸 𝑎𝑛𝑑 ̅̅̅̅
𝐵𝐸 are congruent
b. ∠𝐴𝐶𝐸 is a right angle
c. ̅̅̅̅
𝐴𝐶 𝑎𝑛𝑑 ̅̅̅̅
𝐷𝐸 are parallel
d. ∠𝐴 and ∠𝐵 are congruent
G-CO.6
21. Triangle ABC is located in the third quadrant of a coordinate plane. If triangle ABC is reflected across
the y-axis to obtain triangle, A’B’C’, which statement is true?
a. ∆𝐴′𝐵′𝐶′ lies in quadrant II and is congruent to ∆𝐴𝐵𝐶
b. ∆𝐴′𝐵′𝐶′ lies in quadrant IV and is congruent to ∆𝐴𝐵𝐶
c. ∆𝐴′𝐵′𝐶′ lies in quadrant II and is not congruent to ∆𝐴𝐵𝐶
d. ∆𝐴′𝐵′𝐶′ lies in quadrant IV and is not congruent to ∆𝐴𝐵𝐶
G-CO.6
22. Triangle XYZ is translated by the rule (𝑥 + 3, 𝑦 − 2) and then reflected over the x-axis to create the
triangle X’Y’Z’. Which statement is true?
a. ∆𝑋′𝑌′𝑍′ is a 90° clockwise rotation of ∆𝑋𝑌𝑍
b. ∆𝑋𝑌𝑍 is similar to and congruent to ∆𝑋′𝑌′𝑍′
c. ∆𝑋′𝑌′𝑍′ is a 180° clockwise rotation of ∆𝑋𝑌𝑍
d. ∆𝑋𝑌𝑍 is similar to but not congruent to ∆𝑋′𝑌′𝑍′
MATH 2 UNIT 4 TEST
G-CO.7
23. Use the given triangles to answer the question.
Triangle JKL is reflected across line a to form triangle MNO. Which one of these is true?
a. ̅̅̅
𝐽𝐾 ≅ ̅̅̅̅̅
𝑀𝑂, ̅̅̅̅
𝐾𝐿 ≅ ̅̅̅̅
𝑁𝑂 , 𝑎𝑛𝑑 ∠𝐿 ≅ ∠𝑀
̅̅̅̅̅
̅̅̅
̅̅̅̅̅
̅
b. 𝐽𝐾 ≅ 𝑀𝑁, 𝐽𝐿 ≅ 𝑂𝑀, 𝑎𝑛𝑑 ∠𝐽 ≅ ∠𝑁
̅̅̅̅ ≅ ̅̅̅̅̅
c. ̅̅̅
𝐽𝐾 ≅ ̅̅̅̅
𝑁𝑂, 𝐾𝐿
𝑀𝑁, 𝑎𝑛𝑑 ∠𝐿 ≅ ∠𝑂
̅̅̅̅ ≅ ̅̅̅̅
d. ̅̅̅
𝐽𝐾 ≅ ̅̅̅̅̅
𝑀𝑁, 𝐾𝐿
𝑁𝑂, 𝑎𝑛𝑑 ∠𝐾 ≅ ∠𝑁
G-CO.7
24. Which figure contains two congruent triangles?
a.
b.
c.
d.
G-CO.8
25. Triangles MNO and RST are shown.
Which theorem could be used to prove that ∆𝑀𝑁𝑂 ≅ ∆𝑅𝑆𝑇?
a. Angle-Side-Angle (ASA)
b. Side-Angle-Side (SAS)
c. Side-Side-Angle (SSA)
d. Side-Side-Side (SSS)
MATH 2 UNIT 4 TEST
G-CO.8
26. ∆𝐴𝐵𝐶 undergoes several rigid motions resulting in ∆𝐷𝐸𝐹 as shown below.
Which theorem justifies the statement ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹 ?
a. Angle-Side-Angle
b. Hypotenuse-Leg
c. Side-Angle-Side
d. Side-Side-Side
G-CO.8
27. Javier is writing the following proof:
Which of the following is the reason for statement 5?
a. SSS
b. SAS
c. ASA
d. AAS
G-CO.9
̅̅̅̅ is the perpendicular bisector of 𝐶𝐵
̅̅̅̅.
28. In the figure below, 𝐴𝐷
Based on this information, which other statement can be proven to be true?
a. ̅̅̅̅
𝐴𝐷 ≅ ̅̅̅̅
𝐶𝐵
̅̅̅̅
b. 𝐴𝐵 ≅ ̅̅̅̅
𝐴𝐶
̅̅̅̅ ≅ 𝐶𝐵
̅̅̅̅
c. 𝐴𝐵
̅̅̅̅ ≅ 𝐶𝐵
̅̅̅̅
d. 𝐴𝐶
MATH 2 UNIT 4 TEST
G-CO.9
⃡ as the perpendicular bisector of 𝐴𝐵
̅̅̅̅ such that ∆𝐴𝐶𝐷 and ∆𝐵𝐶𝐷 are
29. John draws ∆𝐴𝐵𝐷 with 𝐶𝐷
congruent to each other.
Which statement can John use this figure to prove?
a. Every isosceles triangle is a right triangle.
b. The base angles of any triangle are congruent.
c. The points on the perpendicular bisector of a side of a triangle are equidistant from all of the vertices
of the triangle.
d. The points on the perpendicular bisector of a side of a triangle are equidistant from the vertices of the
side it bisects.
G-CO.9
30. If 𝑚∠𝐴𝐷𝐵 = 𝑚∠𝐵𝐷𝐶 𝑎𝑛𝑑 ̅̅̅̅
𝐶𝐷 ⊥ ̅̅̅̅
𝐴𝐸 , which is a valid conclusion?
I
II
III
̅̅̅̅ 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐴𝐷𝐶
𝐷𝐵
∠𝐴𝐷𝐵 𝑎𝑛𝑑 ∠𝐴𝐷𝐹 are supplementary angles
∠𝐴𝐷𝐵 𝑎𝑛𝑑 ∠𝐵𝐷𝐶 are complementary angles
a. I only
b. I and II
c. I and III
d. I, II, and III
G-CO.9
31. On a set of parallel lines cut by a transversal, 𝑚∠2 = (7𝑥 − 5)° and 𝑚∠6 = (𝑥 + 25)°. Which value
of x could show that ∠2 and ∠6 are corresponding angles, and why?
a. x = 5; Corresponding angles are congruent.
b. x = 20; Corresponding angles are congruent.
c. x = 5; Corresponding angles are supplementary.
d. x = 20; Corresponding angles are supplementary.
MATH 2 UNIT 4 TEST
G-CO.10c
32. Which pair of steps should be interchanged to fix the proof?
a. steps 2 and 3
b. steps 2 and 4
c. steps 3 and 5
d. steps 4 and 5