Quadrilaterals — Flashcards
Gujarat Board · Class 9 · Mathematics
22 flashcards for Quadrilaterals (Gujarat Board Class 9 Mathematics) to test yourself on key terms and facts. Sample: "What is a parallelogram? State its.
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What is a parallelogram? State its basic definition.
Answer
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. It has four sides, four angles, and four vertices, with the special property that opposite sides never meet.
State Theorem 8.1 about diagonals of a parallelogram.
Answer
Theorem 8.1: A diagonal of a parallelogram divides it into two congruent triangles. This can be proved using the ASA (Angle-Side-Angle) congruence rule with alternate angles formed by parallel lines.
What does Theorem 8.2 tell us about opposite sides of a parallelogram?
Answer
Theorem 8.2: In a parallelogram, opposite sides are equal. This means if ABCD is a parallelogram, then AB = DC and AD = BC. This follows from the congruent triangles formed by the diagonal.
State the converse of Theorem 8.2 (Theorem 8.3).
Answer
Theorem 8.3: If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. This is the converse statement - if AB = DC and AD = BC in quadrilateral ABCD, then ABCD is a paral…
What does Theorem 8.4 state about opposite angles in a parallelogram?
Answer
Theorem 8.4: In a parallelogram, opposite angles are equal. If ABCD is a parallelogram, then ∠A = ∠C and ∠B = ∠D. This can be verified by measuring angles in any parallelogram.
State Theorem 8.5 about the converse of opposite angles property.
Answer
Theorem 8.5: If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. This uses the angle sum property of quadrilaterals and properties of parallel lines with transver…
What is the property of diagonals in a parallelogram (Theorem 8.6)?
Answer
Theorem 8.6: The diagonals of a parallelogram bisect each other. If AC and BD are diagonals intersecting at O, then OA = OC and OB = OD. Point O is the midpoint of both diagonals.
State Theorem 8.7 about the converse of diagonal bisection property.
Answer
Theorem 8.7: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. This can be proved by showing that opposite sides become parallel when diagonals bisect each other.
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