Question 10

Question

A)
The picture below shows four parallelograms that have been divided into triangles. For which parallelogram can the triangles be proven congruent using AAS?

(1 point)
Responses

JKLM
JKLM

QRSP
QRSP

WZYX
WZYX

ABCD
ABCD
Question 11
A)Wyatt and Parker are comparing two triangles to determine if they are congruent. For triangle ABC, <B measures 90 degrees and for triangle PQR, <Q is a right angle. They also know that AB¯¯¯¯¯¯¯¯ ≅QR¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯ ≅ PR¯¯¯¯¯¯¯¯
. Wyatt says the triangles are congruent by the HL Congruence Theorem and Parker thinks that they are congruent by SAS. Who is correct? (Hint: Draw a picture)(1 point)
Responses

Wyatt is correct
Wyatt is correct

Both are wrong, the triangles are not congruent
Both are wrong, the triangles are not congruent

Both are wrong, the triangles are congruent by SSA
Both are wrong, the triangles are congruent by SSA

Parker is correct
Parker is correct
Question 12
A)
If CA¯¯¯¯¯¯¯¯ = 84
and BC¯¯¯¯¯¯¯¯=85
and △ABC ≅ △ CDA
fill in the following information. Note: The drawings are not to scale

(4 points)
AD¯¯¯¯¯¯¯¯=
$$

CD¯¯¯¯¯¯¯¯=
$$

Question 13
A)
What transformations need to be done in order show that △ABC≅△EFD
by mapping ABC on top of EFD? Check all that apply

(4 points)
Responses

Translation
Translation

Rotation
Rotation

Reflection
Reflection

Dilation
Dilation
B)What theorem does this justify?(1 point)
Responses

HL
HL

ASA
ASA

SSA
SSA

AAS
AAS

SAS
SAS

SSS
SSS
Question 14
A)
What two transformations need to be perfomed to show that the triangles are congruent?



(2 points)
Responses

Rotation
Rotation

Reflection
Reflection

Dilation
Dilation

Translation
Translation
B)What congruency theorem does this justify?(1 point)
Responses

AAS
AAS

AAA
AAA

SSS
SSS

HL
HL

ASA
ASA
Question 15
A)
For the picture below: XY = 8, CD = 8. <X = 87 degrees, <Z=57 degrees, <D = 36 degrees and <B = 57 degrees.

Part 1. Explain how you can use the Triangle Sum theorem and the AAS congruency theorem to prove the two triangles congruent. (2pts)

Part 2. Write a correct congruency statement. You may use the = instead of the congruency symbol. (2pts)

Answer 1

Question 10

A) The triangles can be proven congruent using AAS in the parallelogram ABCD.

Question 11

A) Wyatt is correct. They are congruent by the HL Congruence Theorem (Hypotenuse-Leg) because both have a right angle, and the legs are congruent.

Question 12

A) Given the congruence △ABC ≅ △CDA:

• AD = 85
• CD = 84

Question 13

A) The transformations needed to show that △ABC≅△EFD are:

• Translation
• Rotation

B) This justifies the SSS (Side-Side-Side) congruence theorem or could be seen as a combination of transformations leading to congruence, typically referencing side lengths.

Question 14

A) The two transformations needed to show that the triangles are congruent are:

• Reflection
• Translation

B) This justifies the ASA (Angle-Side-Angle) congruency theorem.

Question 15

Part 1: To prove the two triangles congruent, you can apply the Triangle Sum Theorem. For Triangle XYZ, you can calculate the third angle:

• The measure of angle Y can be found as follows: \(180 - (87 + 57) = 36\) degrees. So the angles in Triangle XYZ are 87 degrees, 57 degrees, and 36 degrees. The angles in Triangle DAB are provided as \( <D = 36 \), \( <B = 57 \). Using the AAS congruency theorem, where two angles and the included side are congruent, if we establish that these angles correspond to the angles in Triangle DAB, we can conclude the triangles are congruent.

Part 2: The correct congruency statement is: \( \triangle XYZ = \triangle DAB \).