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Example 1

A second type of special quadrilateral is a rectangle . A rectangle is a quadrilateral with four right angles. 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. Example 1.

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Example 1

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  1. A second type of special quadrilateral is a rectangle. A rectangleis a quadrilateral with four right angles. 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.

  2. Example 1 Carpentry The rectangular gate has diagonal braces. Find HJ. Rect.  diags.  HJ = GK = 48 Def. of  segs. Find HK. Rect.  diags.  Rect.  diagonals bisect each other JL = LG Def. of  segs. JG = 2JL = 2(30.8) = 61.6 Substitute and simplify.

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

  4. Example 2a CDFG is a rhombus. Find CD. CG = GF Def. of rhombus 5a =3a + 17 Substitute a =8.5 Simplify GF = 3a + 17=42.5 Substitute CD = GF Def. of rhombus CD = 42.5 Substitute

  5. Example 2b CDFG is a rhombus. Find the measure. mGCH if mGCD = (b + 3)° and mCDF = (6b – 40)° mGCD + mCDF = 180° b + 3 + 6b –40 = 180° Rhombus  each diag. bisects opp. s 7b = 217° mGCH + mHCD = mGCD b = 31° 2mGCH = mGCD 2mGCH = (b + 3) 2mGCH = (31 + 3) mGCH = 17°

  6. A square is a quadrilateral with four right angles and four congruent sides. In the exercises, you will show that a square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three. Example 3: Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other.

  7. Step 2 Show that EG and FH are perpendicular. Step 1 Show that EG and FH are congruent. Since EG = FH, Since ,

  8. Step 3 Show that EG and FH are bisect each other. Since EG and FH have the same midpoint, they bisect each other. The diagonals are congruent perpendicular bisectors of each other.

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