Question

In the given figure, RV = VT, QV = VU, VR is perpendicular to SQ and VT is perpendicular to SU. Prove that SQ = SU.

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Answer 1

Answer:

Proven that, SQ = SU

Step-by-step explanation:

In the given figure,

RV = VT, QV = VU, VR is perpendicular to SQ and VT is perpendicular to SU.

ΔVRT is a isosceles triangle, ∠R = ∠T = $\frac{1}{2}$ (180° - ∠V)

Similarly, ΔVQU is a isosceles triangle, ∠VQU = ∠VUQ = $\frac{1}{2}$ (180° - ∠V)

Now, ∠SQV = 90° = ∠SUV

∠SQU = 90° - ∠VQU = 90° - ∠VUQ = ∠SUQ

∴ ΔSQU is a isosceles triangle.

∴ SQ = SU [Proven]