[6-4] Properties of Rhombuses, Rectangles, and Squares

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Properties of Rhombuses, Rectangles, and Squares

Presentation transcript:

[6-4] Properties of Rhombuses, Rectangles, and Squares Mr. Joshua Doudt Geometry (H) Pg. 375 - 382

Objective To define and classify special types of parallelograms To use properties of diagonals of rhombuses and rectangles

Lesson Vocabulary Rhombus Rectangle Square

Definition A rhombus is a parallelogram with four congruent sides. A rectangle is parallelogram with four right angles. A square is a parallelogram with four congruent sides and four right angles.

Theorem 6-13 If a parallelogram is a rhombus, then its diagonals are perpendicular.

Theorem 6-14 If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

Proof of Theorem 6-13 Given: ABCD is a rhombus Prove: The diagonals of ABCD are perpendicular Statement: A and C are equidistant from B and D; B and D are equidistant from A and C. A and C are on the perpendicular bisector of 𝐵𝐷 , and B and D are on the perp. Bisector of 𝐴𝐶 𝐴𝐶 ⊥ 𝐵𝐷 Proof: All sides of Rhombus are congruent Converse of the perpendicular bisector theorem Through 2 points, there is one unique line perpendicular to a given line. C B A D

Finding Angle Measures What are the measures of the numbered angles in rhombus ABCD? C B A D 58 1 2 4 3

Theorem 6-13 If a parallelogram is a rectangle, then its diagonals are congruent.

Finding diagonal length In rectangle ABCD, AC = 2𝑥+15 and 𝐷𝐵=5𝑥−12. What is the length of a diagonal?

Joke Time Why did the cowboy adopt a weiner dog? He wanted to get a long little doggy! What do you call a bear with no teeth? A gummy bear! What did 0 say to 8? Nice belt.

Homework Pg. 379 #7-23