## RS Aggarwal Class 9 Solutions Chapter 9 Quadrilaterals and Parallelograms Ex 9C

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Class 9 Solutions Chapter 9 Quadrilaterals and Parallelograms Ex 9C.

**Other Exercises**

- RS Aggarwal Solutions Class 9 Chapter 9 Quadrilaterals and Parallelograms Ex 9A
- RS Aggarwal Solutions Class 9 Chapter 9 Quadrilaterals and Parallelograms Ex 9B
- RS Aggarwal Solutions Class 9 Chapter 9 Quadrilaterals and Parallelograms Ex 9C

**Question 1.**

**Solution:**

Given : In trapezium ABCD,

AB || DC and E is the midpoint of AD.

A line EF ||AB is drawn meeting BC at F.

To prove : F is midpoint of BC

**Question 2.**

**Solution:**

Given : In ||gm ABCD, E and F are the mid points of AB and CD respectively. A line segment GH is drawn which intersects AD, EF and BC at G, P and H respectively.

To prove : GP = PH

**Question 3.**

**Solution:**

Given : In trapezium ABCD, AB || DC

P, Q are the midpoints of sides AD and BC respectively

DQ is joined and produced to meet AB produced at E

Join AC which intersects PQ at R.

**Question 4.**

**Solution:**

Given : In ∆ ABC,

AD is the mid point of BC

DE || AB is drawn. BE is joined.

To prove : BE is the median of ∆ ABC.

Proof : In ∆ ABC

**Question 5.**

**Solution:**

Given : In ∆ ABC, AD and BE are the medians. DF || BE is drawn meeting AC at F.

To prove : CF = \(\frac { 1 }{ 4 } \) BC.

**Question 6.**

**Solution:**

Given : In ||gm ABCD, E is mid point of DC.

EB is joined and through D, DEG || EB is drawn which meets CB produced at G and cuts AB at F.

To prove : (i)AD = \(\frac { 1 }{ 2 }\) GC

**Question 7.**

**Solution:**

Given : In ∆ ABC,

D, E and F are the mid points of sides BC, CA and AB respectively

DE, EF and FD are joined.

**Question 8.**

**Solution:**

Given : In ∆ ABC, D, E and F are the mid points of sides BC, CA and AB respectively

**Question 9.**

**Solution:**

Given : In rectangle ABCD, P, Q, R and S are the midpoints of its sides AB, BC, CD and DA respectively PQ, QR, RS and SP are joined.

To prove : PQRS is a rhombus.

**Question 10.**

**Solution:**

Given : In rhombus ABCD, P, Q, R and S are the mid points of sides AB, BC, CD and DA respectively PQ, QR, RS and SP are joined.

**Question 11.**

**Solution:**

Given : In square ABCD, P,Q,R and S are the mid points of sides AB, BC, CD and DA respectively. PQ, QR, RS and SP are joined.

**Question 12.**

**Solution:**

Given : In quadrilateral ABCD, P, Q, R and S are the midpoints of PQ, QR, RS and SP respectively PR and QS are joined.

To prove : PR and QS bisect each other

Const. Join PQ, QR, RS and SP and AC

Proof : In ∆ ABC,

But diagonals of a ||gm bisect each other PR and QS bisect each other.

∴ PR and QS bisect each other

**Question 13.**

**Solution:**

Given : ABCD is a quadrilateral. Whose diagonals AC and BD intersect each other at O at right angles.

P, Q, R and S are the mid points of sides AB, BC, CD and DA respectively. PQ, QR, QS and SP are joined.

Hope given RS Aggarwal Class 9 Solutions Chapter 9 Quadrilaterals and Parallelograms Ex 9C are helpful to complete your math homework.

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