In the following figure, ∠AXY = ∠AYX. If BX/AX = CY/AY, show that triangle ABC is isosceles. - Noon Academy

In the following figure, ∠AXY = ∠AYX. If BX/AX = CY/AY, show that triangle ABC is isosceles.

Class 10 | Exercise 15E | ICSE | Maths | Selina | Similarity (With Applications to Maps and Models)

In the following figure, ∠AXY = ∠AYX. If BX/AX = CY/AY, show that triangle ABC is isosceles.

Selina Solutions Concise Class 10 Maths Chapter 15 ex. 15(E) - 7

Solution:

According to the given question,

$\angle AXY\text{ }=~\angle AYX$

So,

$AX\text{ }=\text{ }AY$

[Sides opposite to equal angles are equal.]

Also, from BPT we have

$BX/AX\text{ }=\text{ }CY/AY$

Thus,

$AX\text{ }+\text{ }BX\text{ }=\text{ }AY\text{ }+\text{ }CY$

So,

$AB\text{ }=\text{ }AC$

Therefore,

$\vartriangle ABC$

is an isosceles triangle.

i

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