Question

prove that the medians corresponding to equal sides of an isosceles triangle are equal


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Answer 1

Answer:

You have already learnt about the properties and types of triangles. One of the special types of triangle is the isosceles triangle. Isosceles triangle is a triangle which has two equal sides, no matter in what direction the apex (or peak) of the triangle points. Some pointers about isosceles triangles are:

It has two equal sides.

It has two equal angles, that is, the base angles.

When the third angle is 90 degree, it is called a right isosceles triangle.

In this article, we will state two theorems regarding the properties of isosceles triangles and discuss their proofs.

Isosceles Triangle: Theorems

Theorem 1: Angles opposite to the equal sides of an isosceles triangle are also equal.

Proof: Consider an isosceles triangle ABC where AC = BC. We need to prove that the angles opposite to the sides AC and BC are equal, that is, ∠CAB = ∠CBA.

Isosceles Triangle

We first draw a bisector of ∠ACB and name it as CD.

Now in ∆ACD and ∆BCD we have,

AC = BC (Given)

∠ACD = ∠BCD (By construction)

CD = CD (Common to both)

Thus, ∆ACD ≅∆BCD (By SAS congruency)

So, ∠CAB = ∠CBA (By CPCTC)

Step-by-step explanation:

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