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MM1G3d

Understand, use and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite. MM1G3d. Vocabulary. Parallelogram: A quadrilateral with both pairs of opposite sides parallel.

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MM1G3d

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  1. Understand, use and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite. MM1G3d

  2. Vocabulary • Parallelogram: A quadrilateral with both pairs of opposite sides parallel. • Rhombus: a parallelogram with four congruent sides. • Rectangle: a parallelogram with four right angles. • Square: a parallelogram with four congruent sides and four right angles.

  3. Corollaries • A quadrilateral is a rhombus if and only if it has four congruent sides. • A quadrilateral is a rectangle if and only if it has four right angles. • A quadrilateral is a square if and only if it is a rhombus and a rectangle.

  4. Example 1 • Classify the quadrilateral. This quadrilateral is a rhombus because all sides are congruent. 7 73° 7 7 7

  5. Example 2 • Classify the quadrilateral. The quadrilateral is a rectangle because all angles are right angles. We do not know if it is a square because we do not know if all of the sides are congruent.

  6. Rhombus • A parallelogram is a rhombus if and only if its diagonals are perpendicular.

  7. Rhombus • A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. 53 53 127 127 127 127 53 53

  8. Rectangle • A parallelogram is a rectangle if and only if its diagonals are congruent. A B AC is congruent to BD so ABCD is a rectangle. D C

  9. Example 3 • The diagonals of rectangle EFGH intersect at T. Given that m<GHF = 40° and EG = 16, find the indicated variables. E F Find x. EFGH is a rectangle so the diagonals are congruent. EG = 16 so FH = 16. EFGH is a parallelogram so the diagonals bisect each other. Therefore, x = FT = 8. z T x y H G

  10. Example 3 • The diagonals of rectangle EFGH intersect at T. Given that m<GHF = 40° and EG = 16, find the indicated variables. E F Find y. HT and GT are equal, so the angles opposite them are equal. Therefore, m<GHF = m<HGE. z T x 40 y H G

  11. Example 3 • The diagonals of rectangle EFGH intersect at T. Given that m<GHF = 40° and EG = 16, find the indicated variables. E F Find y. HT and GT are equal, so the angles opposite them are equal. Therefore, m<GHF = m<HGE. Since mGHF = 40°, m<HGE = 40°. z T x 40 40 H G

  12. Example 3 • The diagonals of rectangle EFGH intersect at T. Given that m<GHF = 40° and EG = 16, find the indicated variables. E F Find z. ΔEHG is a right triangle with <H being the right angle. z + 90 + 40 = 180 z + 130 = 180 – 130 – 130 z = 50 z T x 40 H G

  13. Assignment • Textbook: p.319-320 (1-28)

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