Question

If two isosceles triangles have equal bases and equal vertical angles.prove that they are congurent​

Answer 1

Answer:

just use A.S.A Congruence theory

Answer 2

Answer:

Given two triangles ABC and DEF.

Given that vertex angle= ⎳BAC = ⎳EDF= θ

BC = EF = a

Let AB = BC = m ; DE=EF = n

Applying Cosine rule in ∆ABC,

a²= m²+m²-2(m)(m) cos θ

a²= 2m²-2m² cos θ

a²= 2m²(1-cos θ) ——(1)

Similarly, in ∆DEF,

a²= 2n²(1-cos θ) ——(2)

From .eqn (1) and (2),

2m²(1-cos θ)= 2n²(1-cos θ)

m² = n²

m = n

AB = DE and AC= DF

Their included angle θ is same (given)

If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

∴ ∆ ABC ≅ ∆DEF

Step-by-step explanation:

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