Section 6 5 Notes Rhombi and Squares EQ

Section 6. 5 Notes: Rhombi and Squares EQ: What are the properties of the diagonals of rhombi?

Vocab! A parallelogram with all 4 sides ≅ Rhombus Corollary Rhombus Diagonals Theorem Rhombus Opposite Angles Theorem A rhombus has all the properties of a parallelogram plus 2 If a parallelogram is a rhombus, then its diagonals are perpendicular If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles

Example 1 The diagonals of rhombus WXYZ intersect at V. If m∠WZX = 39. 5 , find m∠ZYX. 39. 5°

Example 2 The diagonals of rhombus WXYZ intersect at V. If WX = 8 x – 5 and WZ = 6 x + 3, solve for x.

Examples Example 4: Find the measures of the numbered angles in rhombus DEFG.

You Try! •

Vocab! Parallelogram with 4 ≅ sides and 4 right angles Square Corollary Relationship between parallelogram, Rhombi, Rectangles, and Squares All properties of parallelogram, rectangles and rhombi apply to a square Rectangles Square Rhombi

Theorem 6. 17 Theorem 6. 18 Theorem 6. 19 Theorem 6. 20 If ∠ 1 ≅ ∠ 2 and ∠ 3 ≅ ∠ 4 or ∠ 5 ≅ ∠ 6 and ∠ 7 ≅ ∠ 8, then WXYZ is a rhombus If a quadrilateral is both a rectangle and a rhombus, then it is a square

How to prove a square, rhombus or rectangle for Coordinate Geometry • If lengths of the diagonals are congruent then it’s a rectangle • If the diagonals are perpendicular then it’s a rhombus • If the diagonals are both congruent and perpendicular then is a rhombus, rectangle, and square

Example 6 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.

Example 6 cont. Determine whether parallelogram EFGH is a rhombus, a rectangle, or a square for E(0, – 2), F(– 3, 0), G(– 1, 3), and H(2, 1). List all that apply.