CBSE Class 10-Mathematics: Chapter – 6 Triangles Part 12

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Question 10:

In figure, DEFG is a square and , show that

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Answer:

Given is right-angled at A and DEFG is a square

To prove

Proof: Let

Then,

Also is right-angled at D.

From (i) and (ii), we get

Consider

But =DG=DE

Question 11:

In a quadrilateral ABCD, P, Q, R, S are the mid-points of the sides AB, BC, CD and DA, respectively. Prove that PQRS is a parallelogram.

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Answer:

To Prove: PQRS is a parallelogram

Construction: Join AC

Proof: In

In

From (i) and (ii), we get

Similarly, join B to D and