Asked by Ian
Malik is comparing 2 right triangles. Both triangles have a hypotenuse of 13 units. The first triangle has a leg of 12 units and the other triangle has a leg of 5 units. How could Malik prove that the two triangles are congruent? A. He could use the given side lengths and apply the concept of HL. B. He could apply HL Congruence Theorem because the hypotenuses are congruent and each have a right angle. C. He can conclude that they are congruent because they are both right triangles. D. He could apply the Pythagorean Theorem to find the missing side lengths and then compare corresponding sides to apply HL.
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Answered by
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D.
Use the Pythagorean Theorem: for the triangle with leg 12, the other leg is sqrt(13^2 − 12^2) = sqrt(25) = 5. For the triangle with leg 5, the other leg is sqrt(13^2 − 5^2) = sqrt(144) = 12. Now each right triangle has hypotenuse 13 and a corresponding leg of 12 (and the other leg 5), so they are congruent by the HL theorem.
Use the Pythagorean Theorem: for the triangle with leg 12, the other leg is sqrt(13^2 − 12^2) = sqrt(25) = 5. For the triangle with leg 5, the other leg is sqrt(13^2 − 5^2) = sqrt(144) = 12. Now each right triangle has hypotenuse 13 and a corresponding leg of 12 (and the other leg 5), so they are congruent by the HL theorem.
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