Prove that two isosceles triangles having an angle of one equal to the corresponding angle of the other are similar.

Open in App

Solution

Let ΔABC and ΔPQR be two isosceles triangles such thatand.

Let ... (1)

... (2)

... (3)

Substituting the values of ∠A and ∠Q from (2) and (3) in (1), we get:

and

Hence, in isosceles triangles ΔABC and ΔPQR, if, thenand.

Hence, the two triangles will be similar as they would be equiangular.

Suggest Corrections

Similar questions

State, true or false :
(i) Two similar polygons are necessarily congruent.
(ii) Two congruent polygons are necessarily similar.
(iii) All equiangular triangles are similar.
(iv) All isosceles triangles are similar.
(v) Two isosceles-right triangles are similar.
(vi) Two isosceles triangles are similar if an angle of one is congruent to the corresponding angle of the other.
(vii) The diagonals of a trapezium divide each other into proportional segments.

Q. In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

In two right triangles, one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

An angle in an isosceles triangle is $80^{\circ}$ . Find the other two angles corresponding to equal sides.

Q. For two triangles, if sides of one triangle are proportional to the sides of other triangle, then their corresponding angles are equal and hence the two triangles are similar. This is called ___ similarity.

Join BYJU'S Learning Program

Prove that two isosceles triangles having an angle of one equal to the corresponding angle of the other are similar.

Let ΔABC and ΔPQR be two isosceles triangles such thatand. Let ... (1) ... (2) ... (3) Substituting the values of ∠A and ∠Q from (2) and (3) in (1), we get: and Hence, in isosceles triangles ΔABC and ΔPQR, if, thenand. Hence, the two triangles will be similar as they would be equiangular.