Question 1

Question

Question 1
A)
△ABC≅△ABD
 Using the info provided in the picture below, which theorem proves this?

(1 point)
Responses

ASA Theorem
ASA Theorem

SAS Theorem
SAS Theorem

SSS Theorem
SSS Theorem

HL Theorem
HL Theorem
Question 2
A)
Using the congruence statement △BGH≅△PCF
, which of the following statements is correct?

(1 point)
Responses

It is impossible to tell with the information given. 
It is impossible to tell with the information given.

∠G≅∠C 
∠G≅∠C

∠B≅∠F 
 
∠B≅∠F

∠H≅∠P
∠H≅∠P
Question 3
A)

Mario is trying to prove the SSS congruency theorem using the triangles pictured in image 1 below. He translated △ABC
 to create △A′B′C′
 as shown in image 2 and then performed a rotation to create △A"B"C"
 as shown in image 3. Surprisingly, he found that △A"B"C"
 overlapped △LMN
 without him having to do a reflection. What happened?

(1 point)
Responses

Mario has shown that the trwo triangles are congruent. Three transformations are not always necessary when moving 1 triangle on top of the other. 
Mario has shown that the trwo triangles are congruent. Three transformations are not always necessary when moving 1 triangle on top of the other.

Mario made a mistake. He should have translated △ABC
 so that point B moved to point N, then done a reflection, then a rotation
Mario made a mistake. He should have translated △ABC
 so that point B moved to point N, then done a reflection, then a rotation

Mario has shown that the two triangles are not congruent because if the sequence of transformations is not a translation, a rotation and then a reflection, then there is no way that the triangles can be congruent. 
Mario has shown that the two triangles are not congruent because if the sequence of transformations is not a translation, a rotation and then a reflection, then there is no way that the triangles can be congruent.

Mario made a mistake. He should have completed a reflection before the rotation so that there were three transformations in the sequence, 1 of all three types. 
Mario made a mistake. He should have completed a reflection before the rotation so that there were three transformations in the sequence, 1 of all three types. 
Question 4
A)
What triangle congruency theorem can be used to prove the 2 triangles pictured below are congruent, which the give information?

(1 point)
Responses

AAS
AAS

SAS
SAS

HL
HL

SSS
SSS
Question 5
A)Georgia was shown two triangles that had one pair of congruent angles between two pairs of congruent sides. She preformed a series of rigid transformations in order to map one triangle perfectly on top of the other. What theorem has Georgia show to be true by doing these transformations?(1 point)
Responses

the SSS congruence theorem
the SSS congruence theorem

the CPCTC congruence theorem
the CPCTC congruence theorem

the HL congruence theorem
the HL congruence theorem

the SAS congruence theorem
the SAS congruence theorem
Question 6
A)
What ADDITIONAL information is needed to prove that △ABC≅△EDC
 using SAS if point C is the midpoint of both BD¯¯¯¯¯¯¯¯  and AE¯¯¯¯¯¯¯¯

(1 point)
Responses

∠BAC≅∠DEC
∠BAC≅∠DEC

∠ACB≅∠ECD
∠ACB≅∠ECD

AB¯¯¯¯¯¯¯¯≅ ED¯¯¯¯¯¯¯¯
AB¯¯¯¯¯¯¯¯≅ ED¯¯¯¯¯¯¯¯

BD¯¯¯¯¯¯¯¯≅ DC¯¯¯¯¯¯¯¯
BD¯¯¯¯¯¯¯¯≅ DC¯¯¯¯¯¯¯¯
Question 7
A)
In order to prove that △ABC≅△QRS
 using ASA, what OTHER information is needed?

(1 point)
Responses

AC¯¯¯¯¯¯¯¯≅ QS¯¯¯¯¯¯¯
AC¯¯¯¯¯¯¯¯≅ QS¯¯¯¯¯¯¯

∠A≅∠Q
∠A≅∠Q

∠C≅∠S
∠C≅∠S
Question 8
A)
In order to prove the triangles pictured below congruent using ASA, what is the one piece of additional information that is needed?

(1 point)
Responses

DE¯¯¯¯¯¯¯¯  ≅  DQ¯¯¯¯¯¯¯¯
DE¯¯¯¯¯¯¯¯  ≅  DQ¯¯¯¯¯¯¯¯

∠DCE≅∠DCQ
∠DCE≅∠DCQ

∠E≅∠Q
∠E≅∠Q

CE¯¯¯¯¯¯¯¯  ≅  CQ¯¯¯¯¯¯¯¯
CE¯¯¯¯¯¯¯¯  ≅  CQ¯¯¯¯¯¯¯¯
Question 9
A)
What theorem can be used to prove the triangles congruent using the info given in the picture below?

(1 point)
Responses

SSS
SSS

SAS
SAS

ASA
ASA

AAS
AAS
Question 10
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

GPT-4o mini · Answer

Here are the answers to your questions based on the information provided:

Question 1:
Response: SAS Theorem
The SAS (Side-Angle-Side) theorem can be used to show that △ABC≅△ABD if there are two pairs of sides and the included angle between those sides is congruent.

Question 2:
Response: ∠B≅∠F
From the congruence statement △BGH≅△PCF, the corresponding angles are: ∠B ≅ ∠P, ∠G ≅ ∠C, and ∠H ≅ ∠F, so ∠B≅∠F is correct.

Question 3:
Response: Mario has shown that the two triangles are congruent. Three transformations are not always necessary when moving 1 triangle on top of the other.
If the two triangles overlap fully without needing a reflection, it indicates they are congruent, regardless of the transformations used.

Question 4:
Response: SAS
The SAS (Side-Angle-Side) congruence theorem applies if there are two pairs of congruent sides and the included angle is congruent.

Question 5:
Response: the SAS congruence theorem
Georgia proved the congruence through transformations that meet the SAS criteria.

Question 6:
Response: BD¯¯¯¯¯¯¯¯≅ DC¯¯¯¯¯¯¯¯
This additional information is required to show both triangles share the same side length, which is necessary to apply the SAS theorem.

Question 7:
Response: ∠A≅∠Q
To apply the ASA (Angle-Side-Angle) theorem, you need to know that the angles around the side (AC) are congruent.

Question 8:
Response: ∠E≅∠Q
For ASA, the congruence of the angles must be shown, making it necessary to confirm ∠E≅∠Q.

Question 9:
Response: SAS
Depending on the provided information and the similarity of the angles and sides, the SAS theorem may be utilized to show triangle congruence.

Question 10:
Response: QRSP
This parallelogram can contain triangles that can be shown congruent through the AAS (Angle-Angle-Side) congruence postulate.

Please verify the specific details of your images or references to ensure accuracy relative to the provided responses.