NCERT Solutions Class 8 Maths Chapter 4 — Quadrilaterals

Solution:

Step 1: A quadrilateral can be divided into two triangles by drawing one of its diagonals.

Step 2: Since the sum of interior angles in each triangle is 180°, the sum of angles in the quadrilateral is the sum of angles of these two triangles.

Step 3: Therefore, the sum of interior angles of a quadrilateral is 180° + 180° = 360°.

Solution:

Step 1: A trapezium (or trapezoid) is defined as a quadrilateral with at least one pair of parallel sides.

Step 2: In the CBSE/NCERT context for Class 8, it is typically understood as having exactly one pair of opposite sides parallel.

Step 3: Options A, B, and D describe properties of other quadrilaterals like a rhombus, parallelogram, or general parallelogram, respectively.

Solution:

Step 1: In a parallelogram, opposite sides are equal. So, AB = DC and AD = BC are correct statements.

Step 2: In a parallelogram, opposite angles are equal. So, ∠A = ∠C is a correct statement.

Step 3: The diagonals of a general parallelogram are not necessarily equal in length. They are equal only if the parallelogram is a rectangle or a square. Thus, AC = BD is a mistake for a general parallelogram.

Solution:

Step 1: In a parallelogram, adjacent angles are supplementary, meaning their sum is 180°.

Step 2: Angles P and Q are adjacent angles in parallelogram PQRS.

Step 3: Therefore, ∠P + ∠Q = 180°.

Step 4: Substituting the given value, 75° + ∠Q = 180°, which gives ∠Q = 180° - 75° = 105°.

Solution:

Step 1: A key property of a parallelogram is that its diagonals bisect each other.

Step 2: This means that the point of intersection (O) divides each diagonal into two equal parts.

Step 3: So, for diagonal AC, the segments AO and OC must be equal (AO = OC).

Step 4: Given AO = 5 cm, it directly follows that OC = 5 cm.