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
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter4: Quadrilaterals
Section4.3: The Rectangle, Square, And Rhombus
Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...
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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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