Unit Test — Unit test Answers

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1
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Line segment JL is an altitude in triangle JKM.

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A
JKM is a right triangle because KL + LM = 15.3.
B
JKM is a right triangle because KL + LM = 18.2.
C
JKM is not a right triangle because KL + LM ≠ 15.3.
D
JKM is not a right triangle because KL + LM ≠ 18.2.
2
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Which statements are correct? Select three options.

A
△BCD is similar to △BSR.
B
StartFraction B R Over R D EndFraction = StartFraction B S Over S C EndFraction
Option B
C
If the ratio of BR to BD is , then it is possible that BS = 6 and BC = 3.
Option C
D
(BR)(SC) = (RD)(BS)
E
StartFraction B R Over R S EndFraction = StartFraction B S Over S C EndFraction
Option E
3

Triangle A B C is cut by line segment F G. Line segment F G goes from side A B to side A C. The length of B F is x + 6, the length of F A is x + 1, the length of C G is x + 3, and the length of G A is x minus 1.

Question illustration
A
1
B
3
C
6
D
9
4

Which statements are true? Select two options.

A
∠R corresponds to ∠P'QQ'.
B
∠PQR corresponds to ∠QPQ'.
C
Segment QQ' is parallel to segment PP'.
D
Side RQ corresponds to side QQ'.
E
△PQR ≅ △P'Q'Q
5

Line segment ST is dilated to create line segment S'T' using the dilation rule DQ,2.25.

Question illustration
A
x = 2.25 units
B
x = 2.5 units
C
x = 4.25 units
D
x = 4.5 units
6

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?

A
Yes, they both partition the segment into a 1:3 ratio.
B
Yes, they are both the distance from one endpoint to the other.
Option B
C
No, P is the distance from A to B, and Q is the distance from B to A.
Option C
D
No, Q is closer to A and P is closer to B.
7

Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle.

Question illustration
A
ΔJKM
B
ΔMKL
C
ΔKML
D
ΔLJK
8

Which best explains whether or not all isosceles triangles are similar?

A
All isosceles triangles are similar. Two angles within each triangle are always congruent.
B
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.
C
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.
D
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.
9

Points Q and R are midpoints of the sides of triangle ABC.

Question illustration
A
10 units
B
14 units
C
20 units
D
32 units
10

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

Question illustration
A
–1
B
0
C
2
D
3
11

On a coordinate plane, a line is drawn from point K to point J. Point K is at (9, 2) and point J is at (1, negative 10).

Question illustration
A
–1
B
3
C
7
D
11
12

Triangle ABC will be dilated according to the rule(x,y), where point F is the center of dilation.

Question illustration
A
(-8,-4)
B
(-2,-1)
C
(0, 0)
D
(1, 0)
13

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?

Question illustration
A
StartFraction Y Z Over B C = StartFraction 6 Over 3 EndFraction
Option A
B
∠B ≅ ∠Y
C
StartFraction B C Over Y Z EndFraction = StartFraction 6 Over 3 EndFraction
Option C
D
∠B ≅ ∠Z
14

Triangle MRN is created when an equilateral triangle is folded in half.

Question illustration
A
units
Option A
B
4 units
C
units
Option C
D
8 units
15

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9, the length of T Q is 16, and the length of R Q is x.

Question illustration
A
12 units
B
15 units
C
20 units
D
24 units

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