Quadrilaterals — Flashcards
Maharashtra Board · Class 9 · Mathematics
22 flashcards for Quadrilaterals (Maharashtra Board Class 9 Mathematics) to test yourself on key terms and facts.
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What is a parallelogram? Write its definition.
Answer
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. In parallelogram ABCD, AB ∥ DC and AD ∥ BC.
List the four main properties of a parallelogram.
Answer
1. Opposite sides are congruent (equal) 2. Opposite angles are congruent (equal) 3. Diagonals bisect each other 4. Adjacent angles are supplementary (sum = 180°)…
State the theorem: 'Opposite sides and opposite angles of a parallelogram are congruent.'
Answer
In parallelogram ABCD: - Opposite sides: AB = DC and AD = BC - Opposite angles: ∠A = ∠C and ∠B = ∠D This is proved using congruent triangles formed by drawing a diagonal.
What are the four tests to prove that a quadrilateral is a parallelogram?
Answer
1. Both pairs of opposite sides are congruent 2. Both pairs of opposite angles are congruent 3. Diagonals bisect each other 4. One pair of opposite sides is both parallel and congruent…
Prove: If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram.
Answer
Given: PQRS with PS = QR and PQ = SR Construction: Draw diagonal PR Proof: In △SPR and △QRP, PS = QR, SR = QP, PR = RP (common) ∴ △SPR ≅ △QRP (SSS test) ∴ ∠SPR = ∠QRP (alternate angles) Therefore PS ∥…
What is a rectangle? How is it related to a parallelogram?
Answer
A rectangle is a parallelogram in which all angles are right angles (90°). Since it's a parallelogram, it has all properties of parallelograms plus the additional property that all angles are equal to…
State the special property of diagonals of a rectangle.
Answer
Diagonals of a rectangle are congruent (equal in length). This means in rectangle ABCD, diagonal AC = diagonal BD. This property is in addition to the parallelogram property that diagonals bisect each…
What is a rhombus? Write its definition and special property.
Answer
A rhombus is a parallelogram in which all four sides are congruent (equal). Special property: The diagonals of a rhombus are perpendicular bisectors of each other. This means they bisect each other at…
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