# Important Questions for Chapter 8 - Quadrilaterals

The Important Questions for CBSE class 9th Maths PDF includes complete sets of questions for Maths chapter-wise and topic-wise. It will help you to prepare well for your final exams or any other competitive exams.

**Important questions based on NCERT syllabus for Chapter 8 - Quadrilaterals:**

*Question 1*:Two opposite angles of a parallelogram are (4x−3)° and (57−x)°. Find the measure of each angle of the parallelogram.

*Solution*:

Since opposite angles of a parallelogram are equal.

⇒ (4x–3)° = (57–x)°

5x = 60

x = 12

∴ Two angles are equal to (4x−3)° = (4 × 12 − 3)° = (48−3)° = 45°

The other pair will be equal to 180° - 45° = 135°

[Since adjacent angles are supplementary]

∴ Angles are 45°, 45°, 135° and 135°

*Question 2*: ABCD is a Parallelogram is which P and Q are mid-points of opposite sides AB and CD. If AQ intersects DP at S and BQ intersects CP at R, show that

(i) APCQ is a Parallelogram

(ii) DPBQ is a parallelogram

(iii) PSQR is a parallelogram

*Solution*:

(i) Since ABCD is a parallelogram, AB=DC and AB||DC.

AP = 1/2 AB and QC = 1/2DC

Thus, AP = QC and AP||QC.

Hence, APCQ is a parallelogram.

AQ||PC ------(a) (opposite sides of a parallelogram)

(ii) BP = 1/2 AB and QD = 1/2DC

Thus, BP = QD and BP||QD. Hence, DPBQ is a parallelogram

DP||BQ ---------(b) (opposite sides of a parallelogram)

(iii) From (a) and (b) we have

AQ||PC ⇒ SQ||PR

and DP||BQ ⇒ SP||QR

⇒ PSQR is a parallelogram.

*Question 3*: ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that MD ⊥ AC .

*Solution*:

Given, ABC is a right-angled triangle.

∠C = 90°

And M is the mid-point of AB.

Also, MD ∥ BC

Since, MD ∥ BC and CD is transversal.

∴ ∠ADM = ∠ACB ( Corresponding angles)

But ∠ACB = 90°

∴ ADM = 90°

⇒ MD ⊥ AC