Prove that the bisectors of the base angles of an isosceles triangle are equal.

Question

KnowledgeBoat · Accepted Answer

In isosceles triangle △ ABC, Let AB = AC, ∴ ∠C = ∠B = x (let) [Angles opposite to equal sides are equal] From figure, BD and CE are bisectors of angle B and C. ∴ ∠CBD = and ∠BCE = . ∴ ∠CBD = ∠BCE. In △ CBD and △ BCE, ⇒ ∠CBD = ∠BCE (Proved above) ⇒ ∠C = ∠B (Proved above) ⇒ BC = BC (Common side) ∴ △CBD ≅ △BCE (By A.S.A. axiom) We know that, Corresponding sides of congruent triangle are equal. ∴ BD = CE. Hence, proved that the bisectors of the base angles of an isosceles triangle are equal.

Mathematics

Prove that the bisectors of the base angles of an isosceles triangle are equal.

Triangles

Related Questions

In a triangle ABC, AB = AC and ∠A = 36°. If the internal bisector of ∠C meets AB at point D, prove that AD = BC.

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

In the given figure, AB = AC and ∠DBC = ∠ECB = 90°.
Prove that :
(i) BD = CE
(ii) AD = AE

In triangle ABC; AB = AC. P, Q and R are mid-points of sides AB, AC and BC respectively. Prove that :
(i) PR = QR
(ii) BQ = CP

Mathematics

Prove that the bisectors of the base angles of an isosceles triangle are equal.

Triangles

Related Questions

In a triangle ABC, AB = AC and ∠A = 36°. If the internal bisector of ∠C meets AB at point D, prove that AD = BC.

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

In the given figure, AB = AC and ∠DBC = ∠ECB = 90°.Prove that :(i) BD = CE(ii) AD = AE

In triangle ABC; AB = AC. P, Q and R are mid-points of sides AB, AC and BC respectively. Prove that :(i) PR = QR(ii) BQ = CP

In the given figure, AB = AC and ∠DBC = ∠ECB = 90°.
Prove that :
(i) BD = CE
(ii) AD = AE

In triangle ABC; AB = AC. P, Q and R are mid-points of sides AB, AC and BC respectively. Prove that :
(i) PR = QR
(ii) BQ = CP