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Exploring Quadrilaterals: Types, Properties, and Proofs

Learn about various types of quadrilaterals, special parallelograms, and how to prove if a quadrilateral is a parallelogram using properties and theorems. Explore trapezoids, kites, and their unique characteristics.

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Exploring Quadrilaterals: Types, Properties, and Proofs

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  1. Quadrilaterals

  2. Types of quadrilaterals

  3. Types of parallelograms

  4. Problems

  5. Parallelogram properties

  6. Proving that ABCD is a parallelogram If ABCD is a quadrilateral, then how can we prove that it is also a parallelogram? We must prove that both pairs of opposite sides are parallel. How can we prove that lines are parallel in a quadrilateral? To prove that lines are parallel, we must prove one of the following: 1) Alternate interior angles are congruent. 2) Corresponding angles are congruent. 3) Same side interior angles are supplementary.

  7. Special Parallelograms A Rhombus is a parallelogram with four congruent sides. A Rectangle is a parallelogram with four right angles. A Square is a parallelogram with four congruent sides and four right angles.

  8. If a parallelogram is a RHOMBUS -its diagonals are perpendicular -each diagonal bisects a pair of opposite angles. • If a parallelogram is a RECTANGLE -its diagonals are congruent.

  9. Isosceles Trapezoids and Kites • The base angles of an isosceles trapezoid are congruent. • The diagonals of an isosceles trapezoid are congruent. • The diagonals of a kite are perpendicular.

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