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

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