Unit 6 – Polygons and Quadrilaterals 6.5 Conditions for Special Quads Objective Prove that a given quadrilateral is a rectangle, rhombus, or square.

Conditions for rectangles: Unit 6 – Polygons and Quadrilaterals 6.5 Conditions for Special Quads Conditions for rectangles: 1. If one angle of a parallelogram is 90°, then it is a rectangle. 2. If the diagonals of a parallelogram are , then it is a rectangle.

Conditions for rhombus: Unit 6 – Polygons and Quadrilaterals 6.5 Conditions for Special Quads Conditions for rhombus: If one pair of consecutive sides of a parallelogram are , then it is a rhombus. If the diagonals of a parallelogram are ⊥, then it is a rhombus. If the diagonals of a parallelogram bisect a pair of opposite angles, then it is a rhombus. What must you show for a quadrilateral to be a square?.

Choose the best name for the parallelogram then find the numbered angles. 1. 2. 4. 3.

How to determine if a parallelogram is a rhombus, rectangle or square Unit 6 – Polygons and Quadrilaterals 6.5 Conditions for Special Quads How to determine if a parallelogram is a rhombus, rectangle or square Test the diagonals to determine they are equal, perpendicular or both. If ⊥ then rhombus If ≌ then rectangle If both then square If neither then parallelogram

Unit 6 – Polygons and Quadrilaterals 6.5 Conditions for Special Quads Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply. P(–1, 4), Q(2, 6), R(4, 3), S(1, 1)

Unit 6 – Polygons and Quadrilaterals 6.5 Conditions for Special Quads Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply. W(0, 1), X(4, 2), Y(3, –2), Z(–1, –3)

Objectives Vocabulary Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids Objectives Use properties of kites and trapezoids to solve problems. Vocabulary kite trapezoid base of a trapezoid leg of a trapezoid base angle of a trapezoid isosceles trapezoid midsegment of a trapezoid

Diagonals are perpendicular Theorem Exactly one pair of opp   Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids A kite is a quadrilateral with exactly two pairs of congruent consecutive sides. Theorem Diagonals are perpendicular Theorem Exactly one pair of opp  

Find the measures of the numbered angles of each rhombus. Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids Find the measures of the numbered angles of each rhombus. 1 = 60° Diagonals of rhombus bisect angle Diagonals of rhombus perpendicular to each other 2 = 90° 2 3 4 Angle 3 = 30° Diagonals of rhombus bisect angle Base angles . Angle 3 = 180 - 90 - 60 60° 1

Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids In kite ABCD, mDAB = 54°, and mCDF = 52°. Find all angle measures possible.

Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel sides are called legs. Base angles of a trapezoid are two consecutive angles whose common side is a base. If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the properties of an isosceles trapezoid.

The base angles of an isosceles trapezoid are congruent. Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids Theorem The base angles of an isosceles trapezoid are congruent. The diagonals of an isosceles trapezoid are congruent. If a trapezoid has one pair of base angles congruent, then it is an isosceles trapezoid.

Find the measures of the numbered angles in each isosceles trapezoid. 1. 2. 4. 3.

JN = 10.6, and NL = 14.8. Find KM. KB = 21.9 and MF = 32.7. Find FB. Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids JN = 10.6, and NL = 14.8. Find KM. KB = 21.9 and MF = 32.7. Find FB.

The midsegment is half the sum of the bases. Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs. In Lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid Midsegment Theorem is similar to it. Theorem The midsegment is half the sum of the bases.

Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids Find EF. 15 Find AD.

HOMEWORK: 6.5(434): 9-16,24-26,40 10)rhombus 12)parallelogram 14)parallelogram 16)parallelogram,rhombus 24)18.6 26)6.5 40)rectangle   6.6(444): 13-21(odds),27-31(odds),36,41,43 36)8