Understanding Quadrilateral

10 cm

Step 1: We are given that diagonals of parallelogram ABCD meet at O, and OA = 5 cm. Step 2: We need to find AC (the full diagonal). Step 3: The property of a parallelogram states that diagonals bisect each other. Step 4: This means O is the midpoint of diagonal AC. So OA = OC = 5 cm. Step 5: AC = OA + OC = 5 + 5 = 10 cm. Common mistake: Students forget that bisect means O is the midpoint, so AC = 2 × OA, not OA alone.

120°

Step 1: Each exterior angle of the regular polygon = 60°. Step 2: At any vertex of a polygon, the interior angle and exterior angle form a linear pair. Step 3: Interior angle + Exterior angle = 180°. Step 4: Interior angle = 180° − 60° = 120°. Step 5: Answer is 120°. We can also verify: Number of sides = 360° ÷ 60° = 6 sides (hexagon), and each interior angle of a regular hexagon = 120°. ✓

30 cm

Step 1: In parallelogram ABCD, AB = 9 cm and BC = 6 cm. Step 2: In a parallelogram, opposite sides are equal. So AB = DC = 9 cm and BC = AD = 6 cm. Step 3: Perimeter = AB + BC + CD + DA. Step 4: Perimeter = 9 + 6 + 9 + 6 = 30 cm. Step 5: Answer is 30 cm. Common mistake: Some students add only two sides (9 + 6 = 15) and forget that a parallelogram has 4 sides.

Diagonals are perpendicular bisectors of each other

Step 1: We need to identify the correct property of a rhombus. Step 2: A rhombus is a quadrilateral with all 4 sides equal. Step 3: Let us check each option: All angles equal — this is a property of rectangle/square, not necessarily rhombus. Diagonals equal — this is a property of rectangle. All angles 90° — this is a property of rectangle. Step 4: The correct property is that diagonals of a rhombus bisect each other at right angles (they are perpendicular bisectors of each other). Step 5: This is the most special property of a rhombus that distinguishes it from a general parallelogram.