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Svetradugi [14.3K]
3 years ago
15

Given: △RST ~ △VWX

Mathematics
1 answer:
tatiyna3 years ago
4 0

Answer:

Given

Step-by-step explanation:

Given that: △RST ~ △VWX, TU is the altitude of △RST, and XY is the altitude of △VWX.

Comparing △RST and △VWX;

TU ~ XY (given altitudes of the triangles)

<TUS = <XYW (all right angles are congruent)

<UTS ≅ <YXW (angle property of similar triangles)

Thus;

ΔTUS ≅ ΔXYW (congruent property of similar triangles)

<UTS + <TUS + < UST = <YXW + <XTW + <XWY = 180^{0} (sum of angles in a triangle)

Therefore by Angle-Angle-Side (AAS), △RST ~ △VWX

So that:

\frac{TU}{XY} = \frac{US}{YW} (corresponding side length proportion)

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