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Suppose AABC is an equilateral triangle. Use the HL Theorem to explain why any segment perpendicular to a side from the opposite vertex produces two congruent triangles. Would the same be true if AABC were an isosceles triangle that was not equilateral? Explain. ..... Use the HL Theorem to explain why any segment perpendicular to a side from the opposite vertex produces two congruent triangles. Choose the correct answer below. O A. The perpendicular segment produces two right triangles. This segment is congruent to itself, which means that the right triangles have congruent legs. The perpendicular segment bisects the segment opposite the vertex, so the right triangles have a second congruent leg. By HL, the right triangles are congruent. B. The perpendicular segment produces two right triangles. The perpendicular segment is congruent to the hypotenuses of the right triangles. So, the right triangles have congruent legs and hypotenuses. By HL, the right triangles are congruent. O C. The perpendicular segment produces two right triangles. This segment is the hypotenuse of two right triangles, and it is congruent to itself. The perpendicular segment bisects the segment opposite the vertex, so the right triangles have congruent legs. By HL, the right triangles are congruent. D. The perpendicular segment produces two right triangles. This segment is congruent to itself, which means that the right triangles have congruent legs. Since ABC is equilateral, the hypotenuses of the right triangles are congruent. By HL, the right triangles are congruent.

Suppose AABC is an equilateral triangle. Use the HL Theorem to explain why any segment perpendicular to a side from the opposite vertex produces two congruent triangles. Would the same be true if AABC were an isosceles triangle that was not equilateral? Explain. ..... Use the HL Theorem to explain why any segment perpendicular to a side from the opposite vertex produces two congruent triangles. Choose the correct answer below. O A. The perpendicular segment produces two right triangles. This segment is congruent to itself, which means that the right triangles have congruent legs. The perpendicular segment bisects the segment opposite the vertex, so the right triangles have a second congruent leg. By HL, the right triangles are congruent. B. The perpendicular segment produces two right triangles. The perpendicular segment is congruent to the hypotenuses of the right triangles. So, the right triangles have congruent legs and hypotenuses. By HL, the right triangles are congruent. O C. The perpendicular segment produces two right triangles. This segment is the hypotenuse of two right triangles, and it is congruent to itself. The perpendicular segment bisects the segment opposite the vertex, so the right triangles have congruent legs. By HL, the right triangles are congruent. D. The perpendicular segment produces two right triangles. This segment is congruent to itself, which means that the right triangles have congruent legs. Since ABC is equilateral, the hypotenuses of the right triangles are congruent. By HL, the right triangles are congruent.

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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Suppose AABC is an equilateral triangle. Use the HL Theorem to explain why any segment perpendicular to a side from the opposite vertex produces two congruent triangles. Would the same be true if AABC were an isosceles triangle that was not equilateral? Explain. A Use the HL Theorem to explain why any segment perpendicular to a side from the opposite vertex produces two congruent triangles. Choose the correct answer below. O A. The perpendicular segment produces two right triangles. This segment is congruent to itself, which means that the right triangles have congruent legs. The perpendicular segment bisects the segment opposite the vertex, so the right triangles have a second congruent leg. By HL, the right triangles are congruent. B. The perpendicular segment produces two right triangles. The perpendicular segment is congruent to the hypotenuses of the right triangles. So, the right triangles have congruent legs and hypotenuses. By HL, the right triangles are congruent. O C. The perpendicular segment produces two right triangles. This segment is the hypotenuse of two right triangles, and it is congruent to itself. The perpendicular segment bisects the segment opposite the vertex, so the right triangles have congruent legs. By HL, the right triangles are congruent. D. The perpendicular segment produces two right triangles. This segment is congruent to itself, which means that the right triangles have congruent legs. Since ABC is equilateral, the hypotenuses of the right triangles are congruent. By HL, the right triangles are congruent.
Transcribed Image Text:Suppose AABC is an equilateral triangle. Use the HL Theorem to explain why any segment perpendicular to a side from the opposite vertex produces two congruent triangles. Would the same be true if AABC were an isosceles triangle that was not equilateral? Explain. A Use the HL Theorem to explain why any segment perpendicular to a side from the opposite vertex produces two congruent triangles. Choose the correct answer below. O A. The perpendicular segment produces two right triangles. This segment is congruent to itself, which means that the right triangles have congruent legs. The perpendicular segment bisects the segment opposite the vertex, so the right triangles have a second congruent leg. By HL, the right triangles are congruent. B. The perpendicular segment produces two right triangles. The perpendicular segment is congruent to the hypotenuses of the right triangles. So, the right triangles have congruent legs and hypotenuses. By HL, the right triangles are congruent. O C. The perpendicular segment produces two right triangles. This segment is the hypotenuse of two right triangles, and it is congruent to itself. The perpendicular segment bisects the segment opposite the vertex, so the right triangles have congruent legs. By HL, the right triangles are congruent. D. The perpendicular segment produces two right triangles. This segment is congruent to itself, which means that the right triangles have congruent legs. Since ABC is equilateral, the hypotenuses of the right triangles are congruent. By HL, the right triangles are congruent.
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