1. 6.5 Notes
Rhombi and Squares

2. Diagonals of a Rhombus

3. Example 1

4. Example 1
b) The diagonals of rhombus WXYZ intersect at V. If WX = (8x – 5) and WZ = (6x + 3), solve for x.

5. Squares
A square is a parallelogram with four congruent sides and four right angles.
Recall that a parallelogram with four right angles is a rectangle, and a parallelogram with four congruent sides is a rhombus. Therefore, a parallelogram that is both a rectangle and a rhombus is also a square.

6. Parallelograms
The Venn diagram summarizes the relationships among parallelograms, rhombi, rectangles, and squares.

7. Conditions for Rhombi and Squares

8. Example 2 Write a paragraph proof.
Given: LMNP is a parallelogram, Ð2, and Ð6
Prove: LMNP is a rhombus.

9. Example 3
Hector is measuring the boundary of a new garden. He wants the garden to be square. He has set each of the corner stakes 6 feet apart. What does Hector need to know to make sure that the garden is square?

10. Example 4
Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square for the given vertices: A(–2, –1), B(–1, 3), C(3, 2), and D(2, –2). List all that apply. Explain.