7-4 Leaning Objectives To learn about the properties of rectangles, rhombuses, and squares and to apply them while solving problems.

7-4 Vocabulary

A rectangle is another special quadrilateral. 7-4 A rectangle is another special quadrilateral. A rectangle is a quadrilateral with four right angles.

7-4 Since a rectangle is a parallelogram, a rectangle “inherits” all the properties of parallelograms.

A rectangular: JK = 50 cm and JL = 86 cm. Find HM. 7-4 Example 1 A rectangular: JK = 50 cm and JL = 86 cm. Find HM.

The rectangular gate has diagonal braces. Find HJ. 7-4 Example 2 The rectangular gate has diagonal braces. Find HJ.

7-4 A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides. Like a rectangle, a rhombus is a parallelogram. So you can apply the properties of parallelograms to rhombuses.

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TVWX is a rhombus. Find TV. 7-4 Example 3: TVWX is a rhombus. Find TV.

TVWX is a rhombus. Find mVTZ. 7-4 Example 4: TVWX is a rhombus. Find mVTZ.

CDFG is a rhombus. Find CD. 7-4 Example 5 CDFG is a rhombus. Find CD.

Example 6 CDFG is a rhombus. Find the measure. 7-4 Example 6 CDFG is a rhombus. Find the measure. mGCH if mGCD = (b + 3)° and mCDF = (6b – 40)°

7-4 A square is a quadrilateral with four right angles and four congruent sides. A square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three.

7-4 Rectangles, rhombuses, and squares are sometimes referred to as special parallelograms. Helpful Hint

Example 7: Verifying Properties of Squares 7-4 Example 7: Verifying Properties of Squares Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other.

7-4 Example 8 The vertices of square STVW are S(–5, –4), T(0, 2), V(6, –3) , and W(1, –9) . Show that the diagonals of square STVW are congruent perpendicular bisectors of each other.

7-4 Example 9

In rectangle CNRT, CN = 35 ft, and NT = 58 ft. Find each length. 7-4 Example 10 In rectangle CNRT, CN = 35 ft, and NT = 58 ft. Find each length. 1. TR 2. CE

PQRS is a rhombus. Find each measure. 7-4 Example 11 PQRS is a rhombus. Find each measure. 3. QP 4. mQRP

Classify the special quadrilateral. 7-4 Example 12 Classify the special quadrilateral.

Find the measures of the numbered angles in Rhombus DEFG. 7-4 Example 13 Find the measures of the numbered angles in Rhombus DEFG.

What is the m ADC and m BCD? 7-4 Example 14 What is the m ADC and m BCD?

Find the measures of the numbered angles in rhombus ABCD. 7-4 Example 15 Find the measures of the numbered angles in rhombus ABCD.

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