Question

Prove that the perpendicular drawn from the vertex of equal angle of an isoceles triangle to the opposite side are equal .

Answer 1

with figure or what yar?

Answer 2

The perpendicular drawn from the vertex of equal angle of an isoceles triangle to the opposite side are equal is proved

Solution:

An isosceles triangle ABC shown below

The figure is attached below

To prove: The perpendicular drawn from the vertex of equal angle of an isoceles triangle to the opposite side are equal

Two perpendicular are drawn from Point B and C on sides AC and AB respectively.

We have to prove that BE = CD

In the triangle BEA and triangle CDA, the similarities are:-

angle BEA = angle CDA  { Both are 90 degree }

angle CAD = angle BAC { common Angle }

BA = CA { sides of an isosceles triangle }

The Angle Angle Side postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

From above we can say the triangle are congruent by AAS criterion

$\Delta B E A \cong \Delta C D A\{\text { By AAS }\}$

So, by using C.P.C.T { corresponding part of congruent triangles}

“Corresponding Parts of Congruent Triangles”. This theorem states that if we take two or more triangles which are congruent to each other then the corresponding angles and the sides of the triangles are also congruent to each other i.e., their corresponding parts are equal to each other

BE = CD  

Hence proved

Learn more about isoceles triangle

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