Question

Assertion : In the given figure, PQRS is a quadrilateral in which PQ || RS and A is the midpoint of QR. On producing PA and SR meet at T then ST = SR + PQ. Reason : If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent ​

Answer 1

Answer:

Construct a line to join diagonal QS

Diagonal QS intersect the line MN at point O

It is given that PQ∥SR and MN∥PQ

We can write it as

PQ∥MN∥SR

Consider △SPQ

We know that MO∥PQ and M is the midpoint to the side SP

O is the midpoint of the line QS

We know that MN∥SR

In △QRS we know that ON∥SR

O is the midpoint of the diagonal QS

Hence, based on the converse mid-point theorem we know that N is the midpoint of QR

therefore it is proved that N is the midpoint of QR

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