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.
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
(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 .
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