6.5 Notes Rhombi and Squares.

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Presentation transcript:

6.5 Notes Rhombi and Squares

Diagonals of a Rhombus

Example 1

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

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.

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

Conditions for Rhombi and Squares

Example 2 Write a paragraph proof. Given: LMNP is a parallelogram, Ð1 @ Ð2, and Ð2 @ Ð6 Prove: LMNP is a rhombus.

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?

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.