# CBSE Class 10-Mathematics: Chapter – 6 Triangles Part 12 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 10**:

In figure, DEFG is a square and , show that

**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.

**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