Question

Two isosceles triangles have equal vertical angles. Show that the triangles are similar. If the ratio between the areas of these two triangles is 16:25, find the ratio between their corresponding altitudes

Answer 1

Step-by-step explanation:

Let ABC,PQR be two isosceles triangle with equal vertical angles.

Let in ΔABC,AB=AC

⇒∠B=∠C=

2

180−∠A

And in ΔPQR,PQ=PR

⇒∠Q=∠R=

2

180−∠P

Given two vertical angles are equal.

∴∠A=∠P

⇒∠B=∠C=∠Q=∠R