1. Unit 2 – Similarity, Congruence, and Proofs
Review Quiz #5
Congruent Triangles

2. ∠𝑈≅∠𝑉 FALSE ∠𝑊≅∠𝑋 FALSE ∠𝑉≅∠𝑋 FALSE ∠𝑉≅∠𝑌 TRUE
Question 1
∆𝑈𝑉𝑊 and ∆𝑋𝑌𝑍 are congruent triangles. Tell whether each statement is true or false.
∠𝑈≅∠𝑉
FALSE
∠𝑊≅∠𝑋
FALSE
∠𝑉≅∠𝑋
FALSE
∠𝑉≅∠𝑌
TRUE

3. Question 2
Which set of equivalent measures does not indicate that two triangles must be congruent?
angle-angle-angle
angle-side-angle
side-angle-side
angle-angle-side
a. angle-angle-angle

4. 𝐴𝐵 ≅ 𝐵𝐶 FALSE 𝐴𝐵 ≅ 𝐸𝐹 FALSE 𝐴𝐶 ≅ 𝐷𝐹 TRUE 𝐴𝐵 ≅ 𝐷𝐹 FALSE
Question 3
∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹 are congruent triangles. Tell whether each statement is true or false.
𝐴𝐵 ≅ 𝐵𝐶
FALSE
𝐴𝐵 ≅ 𝐸𝐹
FALSE
𝐴𝐶 ≅ 𝐷𝐹
TRUE
𝐴𝐵 ≅ 𝐷𝐹
FALSE

5. Question 4
A triangle congruent to ∆𝐴𝐵𝐶 is to be constructed. Only three components are measured. Which three components, if constructed in the order listed, will always create a congruent triangle?
side-side-angle
angle-angle-angle
angle-side-angle
Only the three side lengths can be used to create a congruent triangle.
c. angle-side-angle

6. It cannot be determined if the triangles are congruent.
Question 5
For ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹, the following is given: ∠𝐴≅∠𝐷, ∠𝐵≅∠𝐸, ∠𝐶≅∠𝐹. By which triangle congruence statement can it be concluded that the triangles are congruent?
It cannot be determined if the triangles are congruent.

7. 𝐷𝐸 ≅ 𝑇𝑉 FALSE 𝐷𝐹 ≅ 𝑈𝑉 FALSE 𝐷𝐹 ≅ 𝑇𝑈 FALSE 𝐷𝐸 ≅ 𝑇𝑈 TRUE
Question 6
∆𝐷𝐸𝐹 and ∆𝑇𝑈𝑉 are congruent triangles. Tell whether each statement is true or false.
𝐷𝐸 ≅ 𝑇𝑉
FALSE
𝐷𝐹 ≅ 𝑈𝑉
FALSE
𝐷𝐹 ≅ 𝑇𝑈
FALSE
𝐷𝐸 ≅ 𝑇𝑈
TRUE

8. Question 7
∆𝐷𝐸𝐹 and ∆𝐺𝐻𝐼 are congruent triangles where ∠𝐹≅∠𝐼. Which pairs of congruent components also indicate that the two triangles are congruent?
∠D≅∠G and DF ≅ HI
FE ≅ HI and DE ≅ GH
∠D≅∠G and DF ≅ GI
∠D≅∠G and ∠E≅∠H
c. ∠D≅∠G and DF ≅ GI

9. It cannot be determined if the triangles are congruent.
Question 8
For ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹, the following is given:
∠𝐶≅∠𝐹, 𝐴𝐵 ≅ 𝐷𝐸 , and 𝐵𝐶 ≅ 𝐸𝐹 . By which triangle congruence statement can it be concluded that the triangles are congruent?
It cannot be determined if the triangles are congruent.

10. ∠𝑋≅∠𝑌 FALSE ∠𝐴≅∠𝐵 FALSE ∠𝐴≅∠𝑌 FALSE ∠𝐵≅∠𝑌 TRUE
Question 9
∆𝐴𝐵𝐶 and ∆𝑋𝑌𝑍 are congruent triangles. Tell whether each statement is true or false.
∠𝑋≅∠𝑌
FALSE
∠𝐴≅∠𝐵
FALSE
∠𝐴≅∠𝑌
FALSE
∠𝐵≅∠𝑌
TRUE

11. FALSE ∆𝐹𝐻𝐽≅∆𝑅𝑀𝑃 ∆𝐹𝐽𝐻≅∆𝑀𝑃𝑅 FALSE ∆𝐹𝐻𝐽≅∆𝑀𝑃𝑅 TRUE ∆𝐹𝐻𝐽≅∆𝑅𝑃𝑀 FALSE
Question 10
If there are two triangles for which 𝐹𝐻 ≅ 𝑀𝑃 , 𝐻𝐽 ≅ 𝑃𝑅 , and 𝐹𝐽 ≅ 𝑀𝑅 , tell whether each statement is true or false.
FALSE
∆𝐹𝐻𝐽≅∆𝑅𝑀𝑃
∆𝐹𝐽𝐻≅∆𝑀𝑃𝑅
FALSE
∆𝐹𝐻𝐽≅∆𝑀𝑃𝑅
TRUE
∆𝐹𝐻𝐽≅∆𝑅𝑃𝑀
FALSE

12. For ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹, the following is given:
Question 11
For ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹, the following is given:
∠𝐶≅∠𝐹, 𝐵𝐶 ≅ 𝐸𝐹 , and 𝐴𝐶 ≅ 𝐷𝐹 . By which triangle congruence statement can it be concluded that the triangles are congruent?
SAS

13. For ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹, the following is given:
Question 12
For ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹, the following is given:
𝐴𝐵 ≅ 𝐷𝐸 , 𝐵𝐶 ≅ 𝐸𝐹 , and 𝐴𝐶 ≅ 𝐷𝐹 . By which triangle congruence statement can it be concluded that the triangles are congruent?
SSS

14. Question 13
Which set of equivalent measures does not indicate that two triangles must be congruent?
angle-side-angle
side-angle-side
angle-angle-angle
angle-angle-side
c. angle-angle-angle

15. Question 14
A triangle congruent to ∆𝐷𝐸𝐹 is to be constructed. Only three components are measured. Which three components, if constructed in the order listed, will always create a congruent triangle?
side-angle-side
side-side-angle
angle-angle-angle
Only the three side lengths can be used to create a congruent triangle.
a. side-angle-side

16. For ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹, the following is given:
Question 15
For ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹, the following is given:
∠𝐴≅∠𝐷, ∠𝐵≅∠𝐸, and 𝐴𝐵 ≅ 𝐷𝐸 . By which triangle congruence statement can it be concluded that the triangles are congruent?
ASA