Grade 10 Quadrilateral Proofs Worksheet
A worksheet for Grade 10 students focusing on proving properties of different quadrilaterals including parallelograms, rectangles, rhombuses, and squares.
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Grade 10 Quadrilateral Proofs
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Read each question carefully and provide clear, logical proofs for each statement. Show all your work and justifications.
1. Given quadrilateral ABCD with diagonals AC and BD bisecting each other at point E. Prove that ABCD is a parallelogram.
2. A rectangle is a parallelogram with four angles. The diagonals of a rectangle are .
3. Which of the following is NOT always true for a rhombus?
All four sides are congruent.
The diagonals are perpendicular bisectors of each other.
The diagonals are congruent.
Opposite angles are congruent.
4. Given a quadrilateral JKLM where JK || LM, JM || KL, and JK ≅ KL. Prove that JKLM is a rhombus. If it is also given that ∠J is a right angle, prove that JKLM is a square.
5. A trapezoid is always a parallelogram.
True
False
6. Given an isosceles trapezoid PQRS with bases PQ and RS. Prove that the diagonals PR and QS are congruent.