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Maths Quadrilaterals Class 8 (Ganita Prakash) Assertion and Reason Questions

Assertion Reasoning Quiz · Class 8 · Maths · CBSE

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Chapter 4 Class 8 - Quadrilaterals (Ganita Prakash) | 7 questions | about 6 minutes

Practise Quadrilaterals Class 8 (Ganita Prakash) with Teachoo's Assertion Reasoning Quiz (Class 8 · Maths · CBSE). Practise these questions in a free interactive quiz with answer feedback.

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Question 1 of 7
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Question 1 of 7
Assertion: In a kite ABCD with AB = BC and CD = DA, diagonal BD bisects diagonal AC at 90°.
Reason: The two triangles formed on the two sides of BD can be proved congruent using the equal adjacent sides and the common side BD.
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Question 2 of 7
Assertion (A): The diagonals of a rhombus are strictly always equal in length.
Reason (R): A rhombus is defined as a quadrilateral in which all four sides share the exact same length.
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Question 3 of 7
Assertion: In an isosceles trapezium, the two angles adjacent to the same base are equal.
Reason: The diagonals of every isosceles trapezium are perpendicular.
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Question 4 of 7
Assertion (A): Every square is correctly classified as a rhombus in a geometric Venn diagram.

Reason (R): The diagonals of a square always bisect each other at an exact 90° angle.
RectangleRhombusSquare
A) Both A and R are true and R is the correct explanation of A.
B) Both A and R are true but R is not the correct explanation of A.
C) A is true but R is false.
D) A is false but R is true.
Answer:BSolution:Both statements are true. A square is a rhombus, and the diagonals of a square do bisect at 90°. However, Reason R is NOT the defining explanation for Assertion A. A square is classified as a rhombus specifically because all four of its sides are equal in length. The diagonal behavior is a resulting property, not the fundamental definition.
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Question 5 of 7
Assertion (A):
If one interior angle of a rhombus is 90°, the rhombus mathematically becomes a square.
Reason (R):
In a rhombus, adjacent angles sum to 180° and opposite angles are equal. Therefore, one 90° angle mathematically forces all four angles to be 90°.
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Question 6 of 7
Assertion (A): If all four interior angles of a quadrilateral measure 90°, it is rigorously classified as a rectangle.

Reason (R): In a quadrilateral where all angles are 90°, drawing a diagonal creates congruent triangles via AAS congruence, mathematically proving the opposite sides are equal.
ABCD
A) Both A and R are true and R is the correct explanation of A.
B) Both A and R are true but R is not the correct explanation of A.
C) A is true but R is false.
D) A is false but R is true.
Answer:ASolution:Both statements are true. As established in Deduction 4 of the text, if all angles are 90°, the line splitting the angles (the transversal diagonal) creates alternate interior relationships. By AAS congruence (\(\Delta BAD \cong \Delta DCB\)), opposite sides are proven equal, which fulfills the complete definition of a rectangle.
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Question 7 of 7
Assertion (A):
The diagonals of a square uniquely bisect the interior angles of the square.
Reason (R):
The diagonals of a square are inherently unequal in length, forcing an uneven angular split.
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