Answers1206310 Geometry Sem 1 - HenryIsosceles Triangles

Isosceles Triangles — Unit test Answers

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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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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.
43

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
44

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.
45

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
46

To verify that the transformation is a dilation, Jeremy should also check which of the following? Select three options.

A
QB = QE
Option A
B
QC = CF
C
DE = 2AB
D
AC = EF
Option D
E
if BC = 2.25, then EF = 2.25
47

Line segment AB is dilated to create line segment A'B' using point Q as the center of dilation.

Question illustration
A
1
B
1.25
C
2
D
2.5
48

Which diagram could be used to prove △ABC ~ △DEC using similarity transformations?

A
Triangle A B C is reflected across side A C and then is dilated to form smaller triangle D C E.
Option A
B
Triangle A B C is reflected, translated to the left, and then is dilated to form triangle D C E.
Option B
C
Triangles A B C and D E C are shown. The angle measures differ between the 2 triangles.
Option C
D
Triangles A B C and D E C are connected at point C. The triangles are shaped differently.
Option D
49

In the diagram, DG = 15, GF = 5, EH = 12, and DE = 8.

Question illustration
A
HF is 2 units and GH is 3 units.
B
HF is 3 units and GH is 2 units.
C
HF is 4 units and GH is 2 units.
D
HF is 3 units and GH is 4 units.
50

What is true about the image ΔQ'R'S'? Select three options.Which statements are true?

A
DO,2 (x,y) = (2x, 2y)
B
Side Q'S' lies on a line with a slope of -1.
C
QR is longer than Q'R'.
D
The vertices of the image are closer to the origin than those of the pre-image.
E
The distance from Q' to the origin is twice the distance from Q to the origin.
51

In the diagram, AB is 6 units, BC is 30 units, and AE is 4 units.

Question illustration
A
16 units
B
20 units
C
24 units
D
28 units
52

Read the proof.Given: AEEC; BDDCProve: △AEC ~ △BDC

Question illustration
A
∠ACE ≅ ∠BCD
B
∠EAB ≅ ∠DBC
C
∠EAC ≅ ∠EAC
D
∠CBD ≅ ∠DBC
53

In the diagram, .

Question illustration
A
MN and SR
B
MN and QR
C
∠S ≅ ∠N
D
∠S ≅ ∠O
54

Multiple similarity transformations are performed on a triangle. Which elements must be preserved?

A
orientation
B
side length
C
angle measure
D
overall size

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