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Properties of Rhombuses, Rectangles, and Squares: Lesson 8.4 Corollaries

Explore the defining characteristics of rhombuses, rectangles, and squares through corollaries and theorems. Understand how to identify each quadrilateral based on their unique properties, including congruent sides, right angles, and perpendicular diagonals.

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Properties of Rhombuses, Rectangles, and Squares: Lesson 8.4 Corollaries

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  1. Properties of Rhombuses, Rectangles, and Squares Lesson 8.4

  2. Corollaries • Rhombus Corollary- A quadrilateral is a rhombus if and only if it has four congruent sides. • Rectangle Corollary- A quadrilateral is a rectangle if and only if it has four right angles. • Square Corollary- A quadrilateral is a square if and only if it is a rhombus and a rectangle. (Four Congruent Sides, Four Right Angles.)

  3. Theorem 8.11 • A parallelogram is a rhombus if and only if its diagonals are perpendicular

  4. Theorem 8.12 • A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

  5. Theorem 8.13 • A parallelogram is a rectangle if and only if its diagonals are congruent. B A AC = BD D C

  6. Guided PracticePg. 534-536(#’s 1-4all) Parallelograms Square Rhombus Rectangle

  7. Homework • 2-48even

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