Prove that two right triangles are congruent if a leg and the altitude to hypotenuse of one of the triangles are respectively congruent to a leg and the altitude to the hypotenuse of the other triangle.

Theorem: Two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.

Prove: Let ABC and DEF are the two right triangles. ( shown in below diagram)

Such that, AB =DE, AC = DF and ∠ABC = ∠ DEF = 90°

Prove: Δ ABC ≅ Δ DEF

Since, In Δ ABC,

( by Pythagoras theorem)

Similarly, In triangle DEF,

But, AC= DF ( given)

Therefore,

⇒

⇒ ( AB= DE)

⇒  

⇒ BC= EF

Therefore, By SSS postulate of congruent,

Δ ABC ≅ Δ DEF

a

b

d

step-by-step explanation: