Understand use and prove properties of and relationships

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Understand, use and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus,

Understand, use and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite. MM 1 G 3 D

Vocabulary Parallelogram: A quadrilateral with both pairs of opposite sides parallel. Rhombus: a parallelogram

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.

Corollaries A quadrilateral is a rhombus if and only if it has four congruent

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.

Example 1 Classify the quadrilateral. 7 7 73° 7 7 This quadrilateral is a

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

Example 2 Classify the quadrilateral. The quadrilateral is a rectangle because all angles are

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.

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

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

Rhombus A parallelogram is a rhombus if and only if each diagonal bisects a

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

Rectangle A parallelogram is a rectangle if and only if its diagonals are congruent.

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

Example 3 The diagonals of rectangle EFGH intersect at T. Given that m<GHF =

Example 3 The diagonals of rectangle EFGH intersect at T. Given that m<GHF = 40° and EG = 16, find the indicated variables. E F z T x y H G 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.

Example 3 The diagonals of rectangle EFGH intersect at T. Given that m<GHF =

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

Example 3 The diagonals of rectangle EFGH intersect at T. Given that m<GHF =

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

Example 3 The diagonals of rectangle EFGH intersect at T. Given that m<GHF =

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

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

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

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