ofof Special Parallelograms 6 4 Properties Special Parallelograms

ofof Special Parallelograms 6 -4 Properties Special Parallelograms Warm Up Lesson Presentation Lesson Quiz Holt Geometry

6 -4 Properties of Special Parallelograms Do Now Solve for x. 1. 16 x – 3 = 12 x + 13 2. 2 x – 4 = 90 ABCD is a parallelogram. Find each measure. 3. CD Holt Geometry 4. m C

6 -4 Properties of Special Parallelograms Objectives TSW prove and apply properties of rectangles, rhombuses, and squares. TSW use properties of rectangles, rhombuses, and squares to solve problems. Holt Geometry

6 -4 Properties of Special Parallelograms Vocabulary rectangle rhombus square Holt Geometry

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

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

6 -4 Properties of Special Parallelograms Example 1: Craft Application A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM. Holt Geometry

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

6 -4 Properties of Special Parallelograms Example 3 Carpentry The rectangular gate has diagonal braces. Find HK. Holt Geometry

6 -4 Properties of Special Parallelograms 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

6 -4 Properties of Special Parallelograms Holt Geometry

6 -4 Properties of Special Parallelograms Example 4: Using Properties of Rhombuses to Find Measures TVWX is a rhombus. Find TV. Holt Geometry

6 -4 Properties of Special Parallelograms Example 5: Using Properties of Rhombuses to Find Measures TVWX is a rhombus. Find m VTZ. Holt Geometry

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

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

6 -4 Properties of Special Parallelograms 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

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

6 -4 Properties of Special Parallelograms Example 8: Verifying Properties of Squares Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other. Holt Geometry

6 -4 Properties of Special Parallelograms Holt Geometry

6 -4 Properties of Special Parallelograms Example 9 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

6 -4 Properties of Special Parallelograms Holt Geometry

6 -4 Properties of Special Parallelograms Holt Geometry

6 -4 Properties of Special Parallelograms Holt Geometry

6 -4 Properties of Special Parallelograms Lesson Quiz: Part I A slab of concrete is poured with diagonal spacers. In rectangle CNRT, CN = 35 ft, and NT = 58 ft. Find each length. 1. TR 35 ft Holt Geometry 2. CE 29 ft

6 -4 Properties of Special Parallelograms Lesson Quiz: Part II PQRS is a rhombus. Find each measure. 3. QP 42 Holt Geometry 4. m QRP 51°

6 -4 Properties of Special Parallelograms Lesson Quiz: Part III 5. The vertices of square ABCD are A(1, 3), B(3, 2), C(4, 4), and D(2, 5). Show that its diagonals are congruent perpendicular bisectors of each other. Holt Geometry

6 -4 Properties of Special Parallelograms Lesson Quiz: Part IV 6. Given: ABCD is a rhombus. Prove: Holt Geometry