Quadrilaterals — Flashcards
Telangana Board · Class 9 · Mathematics
20 flashcards for Quadrilaterals (Telangana Board Class 9 Mathematics) to test yourself on key terms and facts.
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In quadrilateral ABCD, ∠A = 85°, ∠B = 95°, ∠C = 75°. Find ∠D.
Answer
Step 1: Use angle sum property of quadrilateral → Sum of all angles = 360°. Step 2: ∠A + ∠B + ∠C + ∠D = 360°. Step 3: 85° + 95° + 75° + ∠D = 360°. Step 4: 255° + ∠D = 360°. Step 5: ∠D = 360° - 255° = …
In parallelogram PQRS, ∠P = 65°. Find all other angles.
Answer
Step 1: In parallelogram, opposite angles are equal → ∠R = ∠P = 65°. Step 2: Adjacent angles are supplementary → ∠P + ∠Q = 180°. Step 3: 65° + ∠Q = 180° → ∠Q = 115°. Step 4: ∠S = ∠Q = 115° (opposite a…
Two adjacent sides of a parallelogram are 8 cm and 12 cm. Find its perimeter.
Answer
Step 1: In parallelogram, opposite sides are equal. Step 2: If adjacent sides are 8 cm and 12 cm, then all four sides are: 8 cm, 12 cm, 8 cm, 12 cm. Step 3: Perimeter = sum of all sides = 8 + 12 + 8 +…
In triangle ABC, D and E are midpoints of AB and AC respectively. If BC = 16 cm, find DE.
Answer
Step 1: Use midpoint theorem → Line joining midpoints of two sides is parallel to third side and half its length. Step 2: DE || BC and DE = (1/2) × BC. Step 3: DE = (1/2) × 16 = 8 cm. Answer: DE = 8 c…
ABCD is a parallelogram. If diagonal AC = 10 cm and diagonal BD = 14 cm intersect at O, find AO and BO.
Answer
Step 1: In parallelogram, diagonals bisect each other. Step 2: O is midpoint of both diagonals. Step 3: AO = (1/2) × AC = (1/2) × 10 = 5 cm. Step 4: BO = (1/2) × BD = (1/2) × 14 = 7 cm. Answer: AO = 5…
Prove that if diagonals of a quadrilateral bisect each other, then it's a parallelogram.
Answer
Step 1: Given ABCD with diagonals AC, BD intersecting at O where AO = OC, BO = OD. Step 2: In triangles AOB and COD: AO = OC (given), BO = OD (given), ∠AOB = ∠COD (vertically opposite). Step 3: △AOB ≅…
In rectangle ABCD, if AB = 12 cm and BC = 9 cm, find the length of diagonal AC.
Answer
Step 1: Rectangle has all angles = 90°. Step 2: Apply Pythagoras theorem in right triangle ABC. Step 3: AC² = AB² + BC². Step 4: AC² = 12² + 9² = 144 + 81 = 225. Step 5: AC = √225 = 15 cm. Answer: AC …
All sides of rhombus PQRS are 13 cm. If diagonal PR = 24 cm, find diagonal QS.
Answer
Step 1: In rhombus, diagonals bisect at right angles. Step 2: Let diagonals intersect at O. PO = 12 cm, SO = QS/2. Step 3: In right triangle POS: PS² = PO² + SO². Step 4: 13² = 12² + SO². Step 5: 169 …
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