**Assertion and Reason Questions for Class 9 Maths Chapter Quadrilaterals**

** Directions: **(a) Assertion and reason are true and reason is the correct explanation of assertion.

(b) Both assertion and reason are true but reason is not the correct explanation of assertion.

(c) Assertion is true but reason is false.

(d) Assertion is false but reason is true.

**Q.1. Assertion : **The angles of a quadrilateral are x^{0}, (x – 10)^{0}, (x + 30)^{0} and (2x)^{0}, the smallest angle is equal to 58^{0}.**Reason : **Sum of the angles of a quadrilateral is 360^{0}.

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Answer: (a)**Q.2. Assertion : **If the diagonals of a parallelogram ABCD are equal, then ∠ABC = 90^{0}.**Reason :** If the diagonals of a parallelogram are equal, it becomes a rectangle.

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Answer: (a)**Q.3. Assertion :** A parallelogram consists of two congruent triangles.**Reason :** Diagonal of a parallelogram divides it into two congruent triangles.

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Answer: (a)**Q.4. Assertion :** ABCD is a square. AC and BD intersect at O. The measure of ∠ABC = 90^{0}.**Reason :** Diagonals of a square bisect each other at right angles.

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Answer: (a) Since, diagonals of a square bisect each other at right angles.**Q.5. Assertion :** ABCD and PQRC are rectangles and Q is a midpoint of AC . Then DP = PC.

**Reason : **The line segment joining the midpoint of any two sides of a triangle is parallel to the third side and equal to half of it.

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Answer: (b)**Q.6. Assertion : **In ΔABC , median AD is produced to X such that AD DX = . Then ABXC is a parallelogram.**Reason : **Diagonals AX and BC bisect each other at right angles

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Answer: (c)**Q.7. Assertion :** The consecutive sides of a quadrilateral have one common point.**Reason : **The opposite sides of a quadrilateral have two common point

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Answer: (c)**Q.8. Assertion : **Two opposite angles of a parallelogram are (3x-2)^{0} and (50-x)^{0}. The measure of one of the angle is 37^{0}.**Reason : **Opposite angles of a parallelogram are equal.

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Answer: (a) Hint: Since, opposite angles of a parallelogram are equal.**Q.9. Assertion : **If the angles of a quadrilateral are in the ratio 2 : 3 : 7 : 6, then the measure of angles are 40^{0}, 60^{0}, 140^{0} 120^{0}, respectively.**Reason : **The sum of the angles of a quadrilateral is 360^{0}.

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Answer: (a)**Q.10. Assertion :** In ΔABC , E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ = QP.**Reason :** Q is the midpoint of AP.