Quadrilaterals

Answer

Step 1: In a parallelogram, opposite angles are equal and adjacent angles are supplementary. Step 2: ∠C = ∠A = 70° (opposite angles) Step 3: ∠A + ∠B = 180° (adjacent angles are supplementary) ∠B = 180

Answer

Step 1: Find midpoint of diagonal AC Midpoint of AC = ((0+6)/2, (0+3)/2) = (3, 1.5) Step 2: Find midpoint of diagonal BD Midpoint of BD = ((4+2)/2, (0+3)/2) = (3, 1.5) Step 3: Since both midpoints are

Answer

Step 1: Area of rhombus = (1/2) × d₁ × d₂, where d₁ and d₂ are the diagonals Step 2: Given PR = 16 cm and QS = 12 cm Step 3: Area = (1/2) × 16 × 12 Step 4: Area = (1/2) × 192 = 96 cm² Answer: Area of

Answer

Use when: Finding area, proving angles, or solving problems involving perpendicular diagonals. Example: In rhombus ABCD, if one diagonal is 8 cm and area is 24 cm² Step 1: Area = (1/2) × d₁ × d₂ 24 =

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Step 1: In a rectangle, all angles are 90° Step 2: Using Pythagorean theorem in triangle ABC: AC² = AB² + BC² Step 3: AC² = 12² + 9² = 144 + 81 = 225 Step 4: AC = √225 = 15 cm Step 5: Similarly, BD =

Answer

Step 1: Apply Mid-point Theorem: Line segment joining midpoints of two sides is parallel to the third side and half its length Step 2: Since D and E are midpoints of AB and AC: DE || BC and DE = (1/2)

Answer

Step 1: Given that opposite sides are equal: AB = DC and AD = BC Step 2: By Theorem 8.3: If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram Step 3: Since AB = DC =

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Step 1: In a square, if diagonal = d, then side = d/√2 Step 2: Side = 10√2/√2 = 10 cm Step 3: Perimeter of square = 4 × side Step 4: Perimeter = 4 × 10 = 40 cm Answer: Perimeter = 40 cm Alternate meth