Question

Given: △RST ~ △VWX

TU and XY are altitudes.
Prove: TU/XY = US/YW
Please provide reasoning. Thank You :)

Answer 1

Given

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:

`(TU)/(XY)` =
`(US)/(YW)` (corresponding side length proportion)