A square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

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Filo · Accepted Answer

Consider △ABC as an isosceles right triangle which is right angled at B so we getAB=BCConsider a square PBSR inscribed in △ABC with ∠B as common so we getPB=BS=SR=RPwe can write it asAB−PB=BC−BSso we getAP=CS.....(1)Consider △APR and △CSRwe know that∠APR=∠CSR=90ofrom the figure we know that the sides of a square are equal PR=SRBy SAS congruence criterion△APR≅△CSRAR=CR (c.p.c.t)So, we know that point R bisects the hypotenuse ACTherefore, it is proved that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

Question Text	A square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.
Answer Type	Text solution:1
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A square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

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