Quadrilaterals
Bihar Board · Class 9 · Mathematics
Flashcards for Quadrilaterals — Bihar Board Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Explore the full setWhat is a quadrilateral and how many sides, angles, and vertices does it have?
Answer
A quadrilateral is a polygon with four sides, four angles, and four vertices. Examples include squares, rectangles, parallelograms, and rhombus.
Define a parallelogram.
Answer
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. In parallelogram ABCD, AB || DC and AD || BC.
State Theorem 8.1 about diagonals of a parallelogram.
Answer
Theorem 8.1: A diagonal of a parallelogram divides it into two congruent triangles. When diagonal AC is drawn in parallelogram ABCD, triangles ABC and CDA are congruent.
How do you prove that a diagonal divides a parallelogram into two congruent triangles?
Answer
In parallelogram ABCD with diagonal AC: ∠BCA = ∠DAC (alternate angles), ∠BAC = ∠DCA (alternate angles), and AC = CA (common side). Therefore, △ABC ≅ △CDA by ASA rule.
State Theorem 8.2 about opposite sides of a parallelogram.
Answer
Theorem 8.2: In a parallelogram, opposite sides are equal. If ABCD is a parallelogram, then AB = DC and AD = BC.
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. If AB = DC and AD = BC in quadrilateral ABCD, then ABCD is a parallelogram.
State Theorem 8.4 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.
State Theorem 8.5 (converse of Theorem 8.4).
Answer
Theorem 8.5: If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. If ∠A = ∠C and ∠B = ∠D in quadrilateral ABCD, then ABCD is a parallelogram.
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