Question

Triangle ABC is similar to triangle PQR. If AD and PM are altitudes of the two triangles, prove that: `(AB)/(PQ) = (AD)/(PM)`.

Answer 1

Given, ΔABC ∼ ΔPQR

AD and PM are altitudes of these two triangles

To prove: `(AB)/(PQ) = (AD)/(PM)`

Proof: Since, ΔABC ∼ ΔPQR

∴ ∠B = ∠Q

`(AB)/(PQ) = (BC)/(QR)`

Now in ΔABD and ΔPQM

∠B = ∠Q

∠D = ∠M     ...(Each 90°)

∴ ΔABD ∼ ΔPQM     ...(AAS axiom)

∴ `(AB)/(PQ) = (AD)/(PM)`   ...(Corresponding sides of Δ's are proportional)