# How Do You Find The Angle Of An Isosceles Triangle

## How Do You Find The Angle Of An Isosceles Triangle

Theorem: Angles opposite to equal sides of an isosceles triangle are equal.

Given: In ∆ABC, AB = AC
To Prove: ∠B = ∠C
Construction: Draw AD, bisector of ∠A
∴ ∠1 = ∠2
∠1 = ∠2        (by construction)
AB = AC
∴ ∠B = ∠C       (c.p.c.t.) Proved.

and BD = DC (c.p.c.t.) ⇒ AD is median
∴ we can say AD is perpendicular bisector of BC or we can say in isosceles ∆, median is angle bisector and perpendicular to base also.

## Angle Of An Isosceles Triangle Example Problems With Solutions

Example 1:    Find ∠BAC of an isosceles triangle in which AB = AC and ∠B = 1/3 of right angle.
Solution:

Example 2:   In isosceles triangle DEF, DE = EF and ∠E = 70° then find other two angles.

Solution:

Example 3:    ∆ABC and ∆DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see fig.). If AD is extended to intersect BC at P. Show that
(i) ∆ABD ≅ ∆ACD
(ii) ∆ABP ≅ ∆ACP
(iii) AP bisects ∠A as well as ∠D
(iv) AP is the perpendicular bisector of BC.

Solution:

Example 4:    Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ∆PQR (see figure ). Show that:
(i) ∆ABM ≅ ∆PQN         (ii) ∆ABC ≅ ∆PQR

Solution: