AnswersRecovery Content Sec Math 1 - Quarter 4 - 202627Triangle Congruence: SAS

Triangle Congruence: SAS — Unit test Answers

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41
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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.
42
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is an altitude in triangle WXZ.

Question illustration
A
XWZ is an obtuse angle.
Option A
B
XWZ is a right angle.
Option B
C
XWZ is congruent to WXY.
Option C
D
XWZ is congruent to XZW.
Option D
43

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
44

Triangle ABC was dilated using the rule .

Question illustration
A
10 units
B
12 units
C
16 units
D
20 units
45

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
46

Consider the two triangles.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
47

On a coordinate plane, Rectangles A B C D and E F G H are shown. The length of side A B is 6 units and the length of side B C is 3 units. The length of side E F is 8 units and the length of side F G is 4 units.

Question illustration
A
Yes, because corresponding sides are parallel and have lengths in the ratio
Option A
B
Yes, because both figures are rectangles and all rectangles are similar.
C
No, because the center of dilation is not at (0, 0).
D
No, because corresponding sides have different slopes.
48

and are midsegments of ΔWXY.

Question illustration
A
11.57 cm
B
12.22 cm
C
12.46 cm
D
14.50 cm
49

Question text not available

Question illustration
A
3 ft
B
4 ft
C
18 ft
D
12 ft
50

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
51

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
52

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
53

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
54

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
55

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.
56

Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D
57

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
58

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.
59

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)
60

Which best explains why all equilateral triangles are similar?

A
All equilateral triangles can be mapped onto each other using dilations.
B
All equilateral triangles can be mapped onto each other using rigid transformations.
C
All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
D
All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.

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