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Warm Up ABCD is a parallelogram. Find each measure. 3. CD 4. m  C

Warm Up ABCD is a parallelogram. Find each measure. 3. CD 4. m  C. 14. 104°. Objectives. Use properties of rectangles, rhombuses, and squares to solve problems.

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Warm Up ABCD is a parallelogram. Find each measure. 3. CD 4. m  C

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  1. Warm Up ABCD is a parallelogram. Find each measure. 3.CD 4. mC 14 104°

  2. Objectives Use properties of rectangles, rhombuses, and squares to solve problems.

  3. Since a rectangle is a parallelogram by Theorem 6-4-1, a rectangle “inherits” all the properties of parallelograms that you learned in Lesson 6-2.

  4.  diags. bisect each other Example 1: Craft Application A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM. Rect.  diags.  KM = JL = 86 Def. of  segs. Substitute and simplify.

  5. A rhombus is another special quadrilateral. A rhombusis a quadrilateral with four congruent sides.

  6. Example 2A: Using Properties of Rhombuses to Find Measures TVWX is a rhombus. Find TV. WV = XT Def. of rhombus 13b – 9=3b + 4 Substitute given values. 10b =13 Subtract 3b from both sides and add 9 to both sides. b =1.3 Divide both sides by 10.

  7. Example 2A Continued TV = XT Def. of rhombus Substitute 3b + 4 for XT. TV =3b + 4 TV =3(1.3)+ 4 = 7.9 Substitute 1.3 for b and simplify.

  8. Example 2B: Using Properties of Rhombuses to Find Measures TVWX is a rhombus. Find mVTZ. mVZT =90° Rhombus  diag.  Substitute 14a + 20 for mVTZ. 14a + 20=90° Subtract 20 from both sides and divide both sides by 14. a=5

  9. Example 2B Continued Rhombus  each diag. bisects opp. s mVTZ =mZTX mVTZ =(5a – 5)° Substitute 5a – 5 for mVTZ. mVTZ =[5(5) – 5)]° = 20° Substitute 5 for a and simplify.

  10. A square is a quadrilateral with four right angles and four congruent sides. A square is a parallelogram, a rectangle, and a rhombus.

  11. Helpful Hint Rectangles, rhombuses, and squares are sometimes referred to as special parallelograms.

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