Geometry Tutor Worksheet 6 Congruent Triangles
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.
̅̅̅̅ ≅ _____; 𝐷𝐸 ̅̅̅̅ ≅ ______; ̅̅̅̅ 𝐷𝐸 𝐸𝐹 ≅ ______
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.
̅̅̅̅ ̅̅̅̅ ≅ ______ 𝐵𝐶 ≅ _____; ̅̅̅̅ 𝐶𝐷 ≅ ______; 𝐵𝐷
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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 ≅ ______ 4 © MathTutorDVD.com
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 ≅ ________ 10 © MathTutorDVD.com
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: 𝐷𝐸 𝐾𝐽; ̅̅̅̅ 𝐷𝐹 ≅ 𝐾𝐼 𝐸𝐹 ≅ 𝐼𝐽
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. 12 © MathTutorDVD.com
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. ̅̅̅ ; ̅̅̅̅ ̅̅̅̅ ≅ ̅𝐻𝐼 ̅̅̅ Answers: ̅̅̅̅ 𝐵𝐶 ≅ 𝐺𝐼 𝐶𝐷 ≅ ̅̅̅̅ 𝐺𝐻; 𝐵𝐷
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 ̅̅̅̅̅ and 𝐵𝐷 ̅̅̅̅ ≅ 𝑀𝐿 ̅̅̅̅. The them to be congruent. The figure shows ̅̅̅̅ 𝐵𝐶 ≅ 𝑀𝐾 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. ̅̅̅̅ ̅̅̅̅̅ ≅ 𝑆𝑇 Answer: 𝐾𝑀
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 ̅ and 𝐻𝐽 ̅ . The congruence of ̅̅̅ ≅ 𝐼𝑆 ̅̅̅̅ ≅ 𝐽𝑆 them to be congruent. The figure shows 𝑇𝐽 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 ̅̅̅̅ and the triangles share ̅̅̅̅ congruent. The figure shows ̅̅̅̅ 𝐵𝐶 ≅ 𝐿𝐶 𝐶𝐷 as a side. The congruence of the third pair of corresponding sides is missing. ̅̅̅̅ ≅ ̅̅̅̅ Answer: 𝐵𝐷 𝐿𝐷
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: ̅̅̅ 𝐶𝐽 ≅ 𝐼𝐽 21 © MathTutorDVD.com
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 ̅̅̅̅ ≅ 𝐵𝐷 ̅̅̅̅, then a right angle in both triangles and then a shared figure shows 𝐴𝐶 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 ̅̅̅̅̅ ≅ 𝑉𝑋 ̅̅̅̅ and 𝑈𝑉 ̅̅̅̅ ≅ 𝑊𝑋 ̅̅̅̅̅. Then 𝑉𝑊 ̅̅̅̅̅ is a shared side in both figure shows 𝑈𝑊 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 ̅̅̅̅ 𝐹𝐸 ≅ ̅̅̅ 𝐺𝐽 and ̅̅̅̅ 𝐷𝐹 ≅ ̅̅̅̅ 𝐺𝐻 , 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.
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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.
̅̅̅̅ ≅ _____; 𝐷𝐸 ̅̅̅̅ ≅ ______; ̅̅̅̅ 𝐷𝐸 𝐸𝐹 ≅ ______
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.
̅̅̅̅ ̅̅̅̅ ≅ ______ 𝐵𝐶 ≅ _____; ̅̅̅̅ 𝐶𝐷 ≅ ______; 𝐵𝐷
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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 ≅ ______ 4 © MathTutorDVD.com
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 ≅ ________ 10 © MathTutorDVD.com
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: 𝐷𝐸 𝐾𝐽; ̅̅̅̅ 𝐷𝐹 ≅ 𝐾𝐼 𝐸𝐹 ≅ 𝐼𝐽
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. 12 © MathTutorDVD.com
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. ̅̅̅ ; ̅̅̅̅ ̅̅̅̅ ≅ ̅𝐻𝐼 ̅̅̅ Answers: ̅̅̅̅ 𝐵𝐶 ≅ 𝐺𝐼 𝐶𝐷 ≅ ̅̅̅̅ 𝐺𝐻; 𝐵𝐷
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 ̅̅̅̅̅ and 𝐵𝐷 ̅̅̅̅ ≅ 𝑀𝐿 ̅̅̅̅. The them to be congruent. The figure shows ̅̅̅̅ 𝐵𝐶 ≅ 𝑀𝐾 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. ̅̅̅̅ ̅̅̅̅̅ ≅ 𝑆𝑇 Answer: 𝐾𝑀
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 ̅ and 𝐻𝐽 ̅ . The congruence of ̅̅̅ ≅ 𝐼𝑆 ̅̅̅̅ ≅ 𝐽𝑆 them to be congruent. The figure shows 𝑇𝐽 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 ̅̅̅̅ and the triangles share ̅̅̅̅ congruent. The figure shows ̅̅̅̅ 𝐵𝐶 ≅ 𝐿𝐶 𝐶𝐷 as a side. The congruence of the third pair of corresponding sides is missing. ̅̅̅̅ ≅ ̅̅̅̅ Answer: 𝐵𝐷 𝐿𝐷
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: ̅̅̅ 𝐶𝐽 ≅ 𝐼𝐽 21 © MathTutorDVD.com
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 ̅̅̅̅ ≅ 𝐵𝐷 ̅̅̅̅, then a right angle in both triangles and then a shared figure shows 𝐴𝐶 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 ̅̅̅̅̅ ≅ 𝑉𝑋 ̅̅̅̅ and 𝑈𝑉 ̅̅̅̅ ≅ 𝑊𝑋 ̅̅̅̅̅. Then 𝑉𝑊 ̅̅̅̅̅ is a shared side in both figure shows 𝑈𝑊 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 ̅̅̅̅ 𝐹𝐸 ≅ ̅̅̅ 𝐺𝐽 and ̅̅̅̅ 𝐷𝐹 ≅ ̅̅̅̅ 𝐺𝐻 , 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.
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