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Are the triangles congruent by the HL Theorem? A

Are the triangles congruent by the HL Theorem? A

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Title: Are the triangles congruent by the HL Theorem?** **Diagram Explanation:** The diagram shows a square with a diagonal line. The square is labeled with points A, B, C, and D, creating two triangles: triangle ABD and triangle BCD. Both triangles are right triangles due to the 90-degree angles at points A and C. The side AD is congruent to side BC (indicated by hash marks). The diagonal line BD is the hypotenuse shared by both triangles. **Question:** Are the triangles congruent by the HL Theorem? **Options:** - ○ Yes - ○ No **Explanation of HL Theorem:** The Hypotenuse-Leg (HL) Theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle.
Transcribed Image Text:**Title: Are the triangles congruent by the HL Theorem?** **Diagram Explanation:** The diagram shows a square with a diagonal line. The square is labeled with points A, B, C, and D, creating two triangles: triangle ABD and triangle BCD. Both triangles are right triangles due to the 90-degree angles at points A and C. The side AD is congruent to side BC (indicated by hash marks). The diagonal line BD is the hypotenuse shared by both triangles. **Question:** Are the triangles congruent by the HL Theorem? **Options:** - ○ Yes - ○ No **Explanation of HL Theorem:** The Hypotenuse-Leg (HL) Theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle.
**Question:** Are the triangles congruent by the HL Theorem? **Diagram Explanation:** The diagram shows two right triangles, ΔDCA and ΔCBA. The triangle ΔDCA shares the side DC with ΔCBA, making it the common hypotenuse for both triangles. Each triangle has one right angle (marked by a square). The leg CA is marked as equal in both triangles. **Answer Options:** - ○ Yes - ○ No
Transcribed Image Text:**Question:** Are the triangles congruent by the HL Theorem? **Diagram Explanation:** The diagram shows two right triangles, ΔDCA and ΔCBA. The triangle ΔDCA shares the side DC with ΔCBA, making it the common hypotenuse for both triangles. Each triangle has one right angle (marked by a square). The leg CA is marked as equal in both triangles. **Answer Options:** - ○ Yes - ○ No
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