unit test review practice

Given △ABC ~ △XYZ, what is the value of cos(Z)?

12/13

The equation cos(35o) = can be used to find the length of . What is the length of ? Round to the nearest tenth.

20.5 in

What is the location of point G, which partitions the directed line segment from D to F into a 5:4 ratio? -1 0 2 3

3

What is the scale factor of the dilation of triangle DEF? 3/10 3/7 7/3 7

3/10

Rectangle ABCD was dilated to create rectangle A'B'C'D' using point R as the center of dilation. If RD = 15, what is RD'? 3 units 5 units 6 units 9 units

5 units

What is the length of ? 58 cm 75 cm 88 cm 116 cm

58 cm

Triangle QRS is to be dilated using the rule . What will be the distance from the center of dilation, P, to the image of S? 2 units 4 units 6 units 8 units

6 units

What is the x-coordinate of the point that divides the directed line segment from K to J into a ratio of 1:3? -1 3 7 11

7

Which best explains whether or not all isosceles triangles are similar? All isosceles triangles are similar. Two angles within each triangle are always congruent. All isosceles triangles are similar. The triangle sum theorem states that the sum of the angles in a triangle is 180°. Therefore, the third angle can always be determined. All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle. All isosceles triangles are not similar. Given only the vertex angle of an isosceles triangle, there is not enough information to determine the measures of the base angles. Therefore, it is not possible to determine if the base angles of one isosceles triangle are congruent to the base angles of another.

All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

Point P partitions the directed segment from A to B into a 1:3 ratio. Q partitions the directed segment from B to A into a 1:3 ratio. Are P and Q the same point? Why or why not? Yes, they both partition the segment into a 1:3 ratio. Yes, they are both the distance from one endpoint to the other. No, P is the distance from A to B, and Q is the distance from B to A. No, Q is closer to A and P is closer to B.

No, P is the distance from A to B, and Q is the distance from B to A.

Triangle PQR was dilated according to the rule DO,2(x,y)(2x,2y) to create similar triangle P'Q'Q. Which statements are true? Check all that apply. ∠R corresponds to ∠P'QQ'. ∠PQR corresponds to ∠QPQ'. Segment QQ' is parallel to segment PP'. Side RQ corresponds to side QQ'. △PQR ≅ △P'Q'Q

a & d

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25o angle with the ground and when the string makes a 45o angle with the ground? Round to the nearest tenth. 14.2 feet 17.1 feet 47.6 feet 55.2 feet

a. 14.2

The statements below can be used to prove that the triangles are similar. ? △ABC ~ △XYZ by the SSS similarity theorem. Which mathematical statement is missing? (some random answer) ∠B ≅ ∠Y bc/yz = 6/3 ∠B ≅ ∠Z

bc/yz = 6/3

Line segment ST is dilated to create line segment S'T' using the dilation rule DQ,2.25. What is x, the distance between points S' and S? x = 2.25 units x = 2.5 units x = 4.25 units x = 4.5 units

x = 2.5 units

To prove that △VWZ ~ △YXZ by the SAS similarity theorem, which other sides or angles should be used? WV and XY WV and ZY ∠VZW ≅ ∠YZX ∠VWZ ≅ ∠YXZ

∠VZW ≅ ∠YZX