Proove that the diagnols of an isosceles trapezium are equal in height detailed proof

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Considering the isosceles trapezium PQRS, whose parallel sides are PS and QR. The base of isosceles trapezium PQRS is PS.

You need to prove that the length of diagonals PR and QS of isosceles trapezium PQRS are equal, hence, you need to prove that the triangles PQR and QRS are...

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Considering the isosceles trapezium PQRS, whose parallel sides are PS and QR. The base of isosceles trapezium PQRS is PS.

You need to prove that the length of diagonals PR and QS of isosceles trapezium PQRS are equal, hence, you need to prove that the triangles PQR and QRS are congruent.

In triangles PQR and QRS, the length of the sides PQ and RS are equal, because the non-parallel sides of isosceles trapezium are equal.

The side QR is common to both triangles and the angles hat(PQR) and hat(QRS) are equal.

Hence, since the pair of corresponding sides and the included angles are equal, yields that the triangles PQR and QRS are congruent (Side Angle Side).

Since the triangles PQR and QRS are congruent, hence, the sides PR and QS are also equal.

Hence, using the congrunce of triangles PQR and QRS yields that the diagonals PR and QS of isosceles trapezium PQRS are equal.

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