AnswersNY-Geometry Term 1 HillcrestUsing Triangle Similarity Theorems

Using Triangle Similarity Theorems — Unit test Answers

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Parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.

Question illustration
A
One-eighth
Option A
B
One-fourth
Option B
C
4
D
8
2
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Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length of O M is 28, the length of M P is y, and the length of P N is 18.

Question illustration
A
16
B
24
C
32
D
36
3

Triangles A B C and A double-prime B double-prime C double-prime connect at point C. Triangle A B C is rotated and then made smaller to form triangle A double-prime B double-prime C double-prime.

Question illustration
A
a rotation and a reflection
B
a translation and a dilation
C
a reflection and a dilation
D
a dilation and a rotation
4

Triangles L M N and P O N connect at point N. Angles L M N and N O P are congruent.

Question illustration
A
because both triangles appear to be equilateral
B
because∠MNL and ∠ONP are congruent angles
C
because one pair of congruent corresponding angles is sufficient to determine similar triangles
D
because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
5

If point P is of the distance from M to N, what ratio does the point P partition the directed line segment from M to N into?

Question illustration
A
4:1
B
4:3
C
4:7
D
4:10
6

Triangle ABC was dilated using the rule .

Question illustration
A
10 units
B
12 units
C
16 units
D
20 units
7

Consider △RST and △RYX.

Question illustration
A
StartFraction R Y Over Y S EndFraction = StartFraction R X Over X T EndFraction = StartFraction X Y Over T S EndFraction
Option A
B
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction
Option B
C
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction R S Over R Y EndFraction
Option C
D
StartFraction R Y Over R X EndFraction = StartFraction R S Over R T EndFraction = StartFraction X Y Over T S EndFraction
Option D
8

Triangle RST was dilated by a scale factor of . The image, triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units.

Question illustration
A
4 units
B
8 units
C
16 units
D
20 units
9

On a coordinate plane, a line is drawn from point A to point B. Point A is at (9, negative 8) and point B is at (negative 6, 7).

Question illustration
A
(2, –1)
B
(4, –3)
C
(–1, 2)
D
(3, –2)
10

Question text not available

Question illustration
A
3 ft
B
4 ft
C
18 ft
D
12 ft
11

Triangles R S T and V U T are connected at point T. Angles R S T and V U T are right angles. The length of side R S is 12 and the length of side S T is 16. The length of side T U is 8 and the length of U V is 6.

Question illustration
A
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U
Option A
B
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction
Option B
C
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U
Option C
D
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction
Option D
12

Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the length of V S is x, the length of R T is x + 4, and the length of T Q is x minus 3.

Question illustration
A
3
B
8
C
10
D
11
13

In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.

Question illustration
A
∠DFE is 4 times greater than ∠GFH.
B
∠FHG is the measure of ∠FED.
Option B
C
∠DFE is congruent to ∠GFH.
D
∠FHG is congruent to ∠EFD.
14

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 and the length of T Q is 16. The length of R T is x.

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

Triangle TVW is dilated according to the ruleDO,(x,y) to create the image triangle T'V'W', which is not shown.

Question illustration
A
T'(-3, 6) and V'(0, 3)
B
T'(-3, 6) and V'(0, 1)
C
T'(-1, 2) and V'(0, 3)
D
T'(-1, 2) and V'(0, 1)
16

and are midsegments of ΔWXY.

Question illustration
A
11.57 cm
B
12.22 cm
C
12.46 cm
D
14.50 cm
17

Read the proof.Given: AB ∥ DEProve: △ACB ~ △DCE

Question illustration
A
AA similarity theorem.
B
SSS similarity theorem.
C
AAS similarity theorem.
D
ASA similarity theorem.
18

Quadrilateral JKLM was dilated according to the ruleDO,(x,y) to create the image quadrilateral J'K'L'M', which is shown on the graph.

Question illustration
A
(0, -4)
B
(0, -1)
C
(0, 0)
D
(0, 4)
19

If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?

A
0.1
B
Option
Option B
C
1
D
10
20

Point P is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of P A is 2 and the length of P B is 3. The Length of A A prime is 4 and the length of B B prime is 5.

Question illustration
A
Yes, it is an enlargement with a scale factor of 3.
B
Yes, it is an enlargement with a scale factor of .
Option B
C
No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
D
No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.

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