Quadrilaterals — Flashcards
Karnataka Board · Class 9 · Mathematics
20 flashcards for Quadrilaterals (Karnataka Board Class 9 Mathematics) to test yourself on key terms and facts.
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In parallelogram ABCD, if ∠A = 70°, find ∠B, ∠C, and ∠D.
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…
Prove that the diagonals of a parallelogram bisect each other using coordinates. Given ABCD with A(0,0), B(4,0), C(6,3), D(2,3).
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…
If PQRS is a rhombus with diagonal PR = 16 cm and QS = 12 cm, find the area of the rhombus.
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 …
When do you use the property that 'diagonals of a rhombus are perpendicular'? Give a worked example.
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 = …
Show that if ABCD is a rectangle with AB = 12 cm and BC = 9 cm, then its diagonals are equal. Find the length of each diagonal.
Answer
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 = …
In triangle ABC, D and E are midpoints of AB and AC respectively. If BC = 14 cm, find DE.
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)…
Prove that ABCD is a parallelogram if AB = DC = 8 cm and AD = BC = 6 cm.
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 = …
Find the perimeter of a square whose diagonal is 10√2 cm.
Answer
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…
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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