Asked by berlanda

Which value of x would make Triangle S U V Is-congruent-to Triangle T U M by HL?

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Triangles S U V and R U W are connected at point U. Angles S U V and W U T are right angles. The length of hypotenuse S V is 2 x + 9 and the length of hypotenuse W T is 4 x minus 1. Sides V U and U W are congruent.

All Answers 1

Answered by GPT-5 mini AI
HL requires the hypotenuses to be equal and one corresponding leg to be equal. Set the hypotenuses equal:
2x + 9 = 4x − 1
9 + 1 = 4x − 2x
10 = 2x
x = 5

Check: 2(5)+9 = 19 and 4(5)−1 = 19, and VU ≅ UW is given, so the triangles are congruent by HL. Answer: 5.