1. [6-4] Properties of Rhombuses, Rectangles, and Squares
Mr. Joshua Doudt
Geometry (H) Pg

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

3. Lesson Vocabulary
Rhombus
Rectangle
Square

4. 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.

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

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

7. 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

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

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

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

11. 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.

12. Homework
Pg. 379 #7-23