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1 © MathTutorDVD.com Geometry Tutor Worksheet 6 Congruent Triangles
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Geometry Tutor
Worksheet 6
Congruent Triangles
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Geometry Tutor - Worksheet 6 – Congruent Triangles
1. Determine whether the two triangles below are congruent. If so, complete the
congruency statements.
𝐷𝐸̅̅ ̅̅ ≅ _____; 𝐷𝐸̅̅ ̅̅ ≅ ______; 𝐸𝐹̅̅ ̅̅ ≅ ______
2. Determine whether the two triangles below are congruent. If so, complete the
congruency statements.
∠𝑆 ≅ ______ ; ∠𝑅 ≅ ______ ; ∠𝑇 ≅ ______
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3. Determine whether the two triangles below are congruent. If so, complete the
congruency statement.
∆𝐴𝐵𝐶 ≅ ________
4. Determine whether the two triangles below are congruent. If so, complete the
congruency statements.
𝐵𝐶̅̅ ̅̅ ≅ _____; 𝐶𝐷̅̅ ̅̅ ≅ ______; 𝐵𝐷̅̅ ̅̅ ≅ ______
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5. Determine if the two triangles in the figure are congruent. If so, give the reason
for congruency (three letters).
6. Determine if the two triangles in the figure are congruent. If so, give the reason
for congruency (three letters).
7. Determine whether the two triangles below are congruent. If so, complete the
congruency statements.
∠𝐴 ≅ ______ ; ∠𝐵 ≅ ______ ; ∠𝐶 ≅ ______
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8. Determine if the two triangles in the figure are congruent. If so, give the reason
for congruency (three letters).
9. Determine if the two triangles in the figure are congruent. If so, give the reason
for congruency (three letters).
10. Determine if the two triangles in the figure are congruent. If so, give the
reason for congruency (three letters).
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11. Determine whether the two triangles below are congruent. If so, complete the
congruency statement.
∆𝑃𝑅𝑄 ≅ ________
12. Determine whether the two triangles below are congruent. If so, complete the
congruency statement.
∆𝑅𝑆𝐼 ≅ ________
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13. Determine whether the two triangles below are congruent. If so, complete the
congruency statement.
∆𝑊𝑉𝑋 ≅ ________
14. Determine whether the two triangles below are congruent. If so, complete the
congruency statement.
∆𝑆𝑇𝑈 ≅ ________
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15. What additional information is needed to show that the two triangles in the
figure are congruent using 𝑆𝐴𝑆? Answer with a congruence statement.
16. What additional information is needed to show that the two triangles in the
figure are congruent using 𝐴𝐴𝑆? Answer with a congruence statement.
17. What additional information is needed to show that the two triangles in the
figure are congruent using 𝐴𝑆𝐴? Answer with a congruence statement.
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18. What additional information is needed to show that the two triangles in the
figure are congruent using 𝑆𝐴𝑆? Answer with a congruence statement.
19. What additional information is needed to show that the two triangles in the
figure are congruent using 𝑆𝑆𝑆? Answer with a congruence statement.
20. What additional information is needed to show that the two triangles in the
figure are congruent using 𝐴𝑆𝐴? Answer with a congruence statement.
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21. Determine whether the two triangles below are congruent. If so, give the
reason and complete the congruency statement.
Reason: ________; ∆𝐴𝐵𝐶 ≅ ________
22. Determine whether the two triangles below are congruent. If so, give the
reason and complete the congruency statement.
Reason: ________; ∆𝐸𝐹𝐷 ≅ ________
23. Determine whether the two triangles below are congruent. If so, give the
reason and complete the congruency statement.
Reason: ________; ∆𝑉𝑊𝑋 ≅ ________
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24. Determine whether the two triangles below are congruent. If so, give the
reason and complete the congruency statement.
Reason: ________; ∆𝐷𝐸𝐹 ≅ ________
25. Determine whether the two triangles below are congruent. If so, give the
reason and complete the congruency statement.
Reason: ________; ∆𝐴𝐵𝐶 ≅ ________
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Answers – Geometry Tutor – Worksheet 6 – Congruent Triangles
1. Determine whether the two triangles below are congruent. If so, complete the
congruency statements.
Match the markings in the figure to find corresponding sides.
Answers: 𝐷𝐸̅̅ ̅̅ ≅ 𝐾𝐽̅̅ ̅; 𝐷𝐹̅̅ ̅̅ ≅ 𝐾𝐼̅̅ ̅; 𝐸𝐹̅̅ ̅̅ ≅ 𝐼�̅�
2. Determine whether the two triangles below are congruent. If so, complete the
congruency statements.
Match the markings in the figure to find corresponding angles.
Answer: ∠𝑆 ≅ ∠𝐾 ; ∠𝑅 ≅ ∠𝐽 ; ∠𝑇 ≅ ∠𝐼
3. Determine whether the two triangles below are congruent. If so, complete the
congruency statement.
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Match the markings in the figure to find corresponding sides and angles.
Answer: ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐶
4. Determine whether the two triangles below are congruent. If so, complete the
congruency statements.
Match the markings in the figure to find corresponding sides.
Answers: 𝐵𝐶̅̅ ̅̅ ≅ 𝐺𝐼̅̅ ̅; 𝐶𝐷̅̅ ̅̅ ≅ 𝐺𝐻̅̅ ̅̅ ; 𝐵𝐷̅̅ ̅̅ ≅ 𝐻𝐼̅̅̅̅
5. Determine if the two triangles in the figure are congruent. If so, give the reason
for congruency (three letters).
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Two sets of consecutive angles are marked as congruent and the two triangles
share a side between those two angles. This situation is 𝐴𝑆𝐴.
Answer: 𝐴𝑆𝐴
6. Determine if the two triangles in the figure are congruent. If so, give the reason
for congruency (three letters).
The two triangles have one set of sides marked as congruent. Then, the triangles
share a vertex with vertical angles at that vertex. Lastly, the next pair of
consecutive angles are marked as congruent. This situation is 𝐴𝐴𝑆.
Answer: 𝐴𝐴𝑆
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7. Determine whether the two triangles below are congruent. If so, complete the
congruency statements.
Match the markings in the figure to find corresponding angles.
Answers: ∠𝐴 ≅ ∠𝐿 ; ∠𝐵 ≅ ∠𝑀 ; ∠𝐶 ≅ ∠𝑁
8. Determine if the two triangles in the figure are congruent. If so, give the reason
for congruency (three letters).
The two triangles show three pairs of angles marked as congruent, but no
information is given about the length of the sides. This situation is 𝐴𝐴𝐴, but the
acceptable means of triangle congruence are 𝑆𝑆𝑆, 𝐴𝐴𝑆, 𝐴𝑆𝐴, and 𝑆𝐴𝑆.
Answer: The triangles are not congruent.
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9. Determine if the two triangles in the figure are congruent. If so, give the reason
for congruency (three letters).
The two triangles have two sets of consecutive angles marked as congruent. Then,
the triangles share a side that is included between the two congruent angles. This
situation is 𝐴𝑆𝐴.
Answer: 𝐴𝑆𝐴
10. Determine if the two triangles in the figure are congruent. If so, give the
reason for congruency (three letters).
The markings on the triangles show one pair of congruent angles, then a pair of
congruent right angles, and lastly, a shared side next to the right angles. This
situation is 𝐴𝐴𝑆.
Answer: 𝐴𝐴𝑆
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11. Determine whether the two triangles below are congruent. If so, complete the
congruency statement.
Match the markings in the figure to find corresponding sides and angles.
Answer: ∆𝑃𝑅𝑄 ≅ ∆𝑄𝐷𝑃
12. Determine whether the two triangles below are congruent. If so, complete the
congruency statement.
Match the markings in the figure to find corresponding sides and angles.
Answer: ∆𝑅𝑆𝐼 ≅ ∆𝑆𝑅𝑇
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13. Determine whether the two triangles below are congruent. If so, complete the
congruency statement.
Match the markings in the figure to find corresponding sides and angles.
Answer: ∆𝑊𝑉𝑋 ≅ ∆𝐷𝐶𝐸
14. Determine whether the two triangles below are congruent. If so, complete the
congruency statement.
Match the markings in the figure to find corresponding sides and angles.
Answer: ∆𝑆𝑇𝑈 ≅ ∆𝐶𝐷𝐸
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15. What additional information is needed to show that the two triangles in the
figure are congruent using 𝑆𝐴𝑆? Answer with a congruence statement.
The congruence method 𝑆𝐴𝑆 requires two sides and the included angle between
them to be congruent. The figure shows 𝐵𝐶̅̅ ̅̅ ≅ 𝑀𝐾̅̅ ̅̅ ̅ and 𝐵𝐷̅̅ ̅̅ ≅ 𝑀𝐿̅̅ ̅̅ . The
congruence of the included angle is missing.
Answer: ∠𝐵 ≅ ∠𝑀
16. What additional information is needed to show that the two triangles in the
figure are congruent using 𝐴𝐴𝑆? Answer with a congruence statement.
The congruence method 𝐴𝐴𝑆 requires two consecutive angles and the next side
to be congruent. The congruence of the first consecutive angle is missing.
Answer: ∠𝐸 ≅ ∠𝑀
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17. What additional information is needed to show that the two triangles in the
figure are congruent using 𝐴𝑆𝐴? Answer with a congruence statement.
The congruence method 𝐴𝑆𝐴 requires two consecutive angles and the included
side to be congruent. The congruence of the included side is missing.
Answer: 𝐾𝑀̅̅ ̅̅ ̅ ≅ 𝑆𝑇̅̅̅̅
18. What additional information is needed to show that the two triangles in the
figure are congruent using 𝑆𝐴𝑆? Answer with a congruence statement.
The congruence method 𝑆𝐴𝑆 requires two sides and the included angle between
them to be congruent. The figure shows 𝑇𝐽̅̅ ̅ ≅ 𝐼�̅� and 𝐻𝐽̅̅̅̅ ≅ 𝐽�̅�. The congruence of
the included angle is missing.
Answer: ∠𝐻𝐽𝑇 ≅ ∠𝐽𝑆𝐼
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19. What additional information is needed to show that the two triangles in the
figure are congruent using 𝑆𝑆𝑆? Answer with a congruence statement.
The congruence method 𝑆𝑆𝑆 requires all three pairs of corresponding sides to be
congruent. The figure shows 𝐵𝐶̅̅ ̅̅ ≅ 𝐿𝐶̅̅̅̅ and the triangles share 𝐶𝐷̅̅ ̅̅ as a side. The
congruence of the third pair of corresponding sides is missing.
Answer: 𝐵𝐷̅̅ ̅̅ ≅ 𝐿𝐷̅̅ ̅̅
20. What additional information is needed to show that the two triangles in the
figure are congruent using 𝐴𝑆𝐴? Answer with a congruence statement.
The congruence method 𝐴𝑆𝐴 requires two consecutive angles and the included
side to be congruent. The figure shows ∠𝐶 ≅ ∠𝐼 and the two triangles have one
set of congruent corresponding angles because of a vertical angle relationship.
The congruence of the included side is missing.
Answer: 𝐶𝐽̅̅ ̅ ≅ 𝐼�̅�
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21. Determine whether the two triangles below are congruent. If so, give the
reason and complete the congruency statement.
Match the markings in the figure to find corresponding sides and angles. The
figure shows 𝐴𝐶̅̅ ̅̅ ≅ 𝐵𝐷̅̅ ̅̅ , then a right angle in both triangles and then a shared
side. This situation is 𝑆𝐴𝑆.
Answer: Reason: 𝑆𝐴𝑆; ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐶𝐵
22. Determine whether the two triangles below are congruent. If so, give the
reason and complete the congruency statement.
Match the markings in the figure to find corresponding sides and angles. When
looking at the figure, the triangles have one pair of sides marked as congruent,
one pair of angles marked congruent, and a shared side. This means the possible
congruence reason uses two sides and one angle, which gives us 𝑆𝐴𝑆. However, a
closer look at the figure reveals that the sides that are marked congruent do not
correspond to each other. Therefore, the triangles are not congruent.
Answer: The triangles are not congruent.
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23. Determine whether the two triangles below are congruent. If so, give the
reason and complete the congruency statement.
Match the markings in the figure to find corresponding sides and angles. The
figure shows 𝑈𝑊̅̅ ̅̅ ̅ ≅ 𝑉𝑋̅̅ ̅̅ and 𝑈𝑉̅̅ ̅̅ ≅ 𝑊𝑋̅̅ ̅̅ ̅. Then 𝑉𝑊̅̅ ̅̅ ̅ is a shared side in both
triangles. This situation is 𝑆𝑆𝑆.
Reason: 𝑆𝑆𝑆; ∆𝑉𝑊𝑋 ≅ ∆𝑊𝑉𝑈
24. Determine whether the two triangles below are congruent. If so, give the
reason and complete the congruency statement.
Match the markings in the figure to find corresponding sides and angles. The
figure shows 𝐹𝐸̅̅ ̅̅ ≅ 𝐺𝐽̅̅ ̅ and 𝐷𝐹̅̅ ̅̅ ≅ 𝐺𝐻̅̅ ̅̅ , then a right angle in both triangles is the
included angle between these sides. This situation is 𝑆𝐴𝑆.
Reason: 𝑆𝐴𝑆; ∆𝐷𝐸𝐹 ≅ ∆𝐻𝐽𝐺
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25. Determine whether the two triangles below are congruent. If so, give the
reason and complete the congruency statement.
The markings on the triangle on the left triangle show 𝑆𝐴𝑆 while the markings on
the right triangle show 𝑆𝑆𝐴, which is not one of the acceptable methods of
proving triangle congruence.
Answer: The triangles are not congruent.
