Question

AX and DY are altitudes of two similar triangles triangle ABC and triangle DEF.prove that AX:DY=AB:DE​

Answer 1

Step-by-step explanation:

Given, Δ ABC ∼ Δ DEF

⇒ ∠ ABC = ∠ DEF

⇒ consider Δ ABX and Δ DEY

⇒ ∠ ABX = ∠ DEY

⇒ ∠ AXB = ∠ DYE = 90°

⇒ ∠ BAX = ∠ EDY

⇒ By A-A-A property we have in two triangles if the angles are equal, then sides opposite to the equal angles are in the same ratio (or proportional) and hence the triangles

⇒ Δ ABX ∼ Δ DEY.

so,

⇒ 

∴ AX:DY = AB:DE

Hence proved