7 4 Properties of Special Parallelograms 6 4

7 -4 Properties of Special Parallelograms 6 -4 Leaning Objectives To learn about the properties of rectangles, rhombuses, and squares and to apply them while solving problems. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Vocabulary Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 A rectangle is another special quadrilateral. A rectangle is a quadrilateral with four right angles. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Since a rectangle is a parallelogram, a rectangle “inherits” all the properties of parallelograms. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Example 1 A rectangular: JK = 50 cm and JL = 86 cm. Find HM. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Example 2 The rectangular gate has diagonal braces. Find HJ. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -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. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Example 3: TVWX is a rhombus. Find TV. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Example 4: TVWX is a rhombus. Find m VTZ. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Example 5 CDFG is a rhombus. Find CD. Holt Geometry

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

7 -4 Properties of Special Parallelograms 6 -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. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Helpful Hint Rectangles, rhombuses, and squares are sometimes referred to as special parallelograms. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Example 7: Verifying Properties of Squares Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -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. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Example 9 Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Example 10 In rectangle CNRT, CN = 35 ft, and NT = 58 ft. Find each length. 1. TR Holt Geometry 2. CE

7 -4 Properties of Special Parallelograms 6 -4 Example 11 PQRS is a rhombus. Find each measure. 3. QP Holt Geometry 4. m QRP

7 -4 Properties of Special Parallelograms 6 -4 Example 12 Classify the special quadrilateral. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Example 13 Find the measures of the numbered angles in Rhombus DEFG. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 What is the m Holt Geometry Example 14 ADC and m BCD?

7 -4 Properties of Special Parallelograms 6 -4 Example 15 Find the measures of the numbered angles in rhombus ABCD. Holt Geometry

7 -4 Properties of Special Parallelograms 6 -4 Holt Geometry