1 / 8

5.10 Properties of Rhombuses, Rectangles, and Squares

5.10 Properties of Rhombuses, Rectangles, and Squares. Vocabulary. 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. Corollaries.

sykesc
Download Presentation

5.10 Properties of Rhombuses, Rectangles, and Squares

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 5.10 Properties of Rhombuses, Rectangles, and Squares

  2. Vocabulary • 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.

  3. 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.

  4. ABCD is a rhombus. ABCD is a rectangle. ABCD is a square.

  5. Q Q a. S S a. By definition, a rhombus is a parallelogram with four congruent sides. By Theorem 8.4, opposite angles of a parallelogram are congruent. So, .The statement is always true. EXAMPLE 1 Use properties of special quadrilaterals For any rhombus QRST, decide whether the statement is always or sometimes true. Draw a sketch and explain your reasoning. SOLUTION

  6. Q b. R • If rhombus QRSTis a square, then all four angles are congruent right angles. So, if QRSTis a square. Because not all rhombuses are also squares, the statement is sometimes true. Q R EXAMPLE 1 Use properties of special quadrilaterals For any rhombus QRST, decide whether the statement is always or sometimes true. Draw a sketch and explain your reasoning. SOLUTION

  7. Theorem 5.26: A parallelogram is a rhombus if and only if its diagonals are perpendicular.Theorem 5.27: A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.Theorem 5.28: A parallelogram is a rectangle if and only if its diagonals are congruent.

More Related