Geo 8.4 & 8.5 Properties of Traps, Kites, Rhombuses, Rectangles, and Squares.notebook

8.4 & 8.5 Properes of Trapezoids, Kites, Rhombuses, Rectangles, and Squares Objecves: 1. You will use properes of trapezoids, kites, rhombuses, rectangles, and squares.

Trapezoid *all the properes of a Quadrilateral Plus..... *exactly 1 pair of parallel sides

D C Isosceles Trapezoid >> *1 pair legs *2 pair base angles >> >> >> *diagonals A B

Kite Vertex *all the properes of a Quadrilateral Angle Plus..... *2 pair of adjacent sides

Non Vertex Non Vertex Angle Angle *diagonals are perpendicular

*vertex diagonal bisects the nonvertex diagonal

Vertex Angle *vertex diagonal bisects the vertex angles

*nonvertex angles congruent

Rectangle

A B *all the properes of a Parallelogram Plus..... *4 right angles

*diagonals are congruent D C

Nov 19­12:10 PM 1 Geo 8.4 & 8.5 Properties of Traps, Kites, Rhombuses, Rectangles, and Squares.notebook

Rhombus *all the properes of a Parallelogram & Kite A B Plus..... *4 sides

D C

Square A B *all the properes of a ll the other Quadrilaterals!

D C

Nov 20­8:45 AM 2 Geo 8.4 & 8.5 Properties of Traps, Kites, Rhombuses, Rectangles, and Squares.notebook

Example 1: Find x & y so that the quadrilateral is a trapezoid.

3x + 10 3y ­ 6

2x + 7 y + 18

3x + 10 + 2x + 7 = 180 3y ­ 6 + y + 18 = 180 5x + 17 = 180 4y + 12 = 180 5x = 163 4y = 168 x = 32.6 y = 42

If x = 32.6 and y = 42, then the consecuve interior angles would be supplementary. This would make one pair of opposite sides parallel and make the quadrilateral a trapezoid.

Example 2: The diagonals of rhombus PQRS intersect at T. Given that m∠RPS = 30° and RT = 6, find the Indicated measure.

a) m∠QPR b) m∠QTP

c) RP d) QT

Example 3: The diagonals of rectangle WXYZ intersect at P. Given that m∠YXZ=50° and XZ=12, find the Indicated measure. a) m∠WXZ b) m∠WPX

c) PY d) WX

Nov 19­12:32 PM 3 Geo 8.4 & 8.5 Properties of Traps, Kites, Rhombuses, Rectangles, and Squares.notebook

Example 4: The diagonals of square DEFG intersect at H. Given that EH=5, find the indicated measure. a) m∠GHF b) m∠DGH

c) HF d) DE

Example 5: a) Find the value of x. b) Find the measure of ∠K and ∠J.

If you connect the midpoints of the two legs of a trapezoid, the resulng segment is known as the ______.midsegment

There are 2 special properes. *parallel to the bases H A *length of the median is half the sum of the two bases N M Midsegment = a+b 2 P R

Dec 1­2:28 PM 4 Geo 8.4 & 8.5 Properties of Traps, Kites, Rhombuses, Rectangles, and Squares.notebook

Example 6: Find the length of median MN in trapezoid TRAP if TR = 12 cm and PA = 18 cm.

Example 7: Solve for the length of MP if quadrilateral P MNOP is a trapezoid. l S l O

59cm 13cm

ll ll M T N

Example 8: Solve for x.

Nov 20­1:46 PM 5 Geo 8.4 & 8.5 Properties of Traps, Kites, Rhombuses, Rectangles, and Squares.notebook

8.4 p.531 #19‐29, 32‐49 AND 8.5 p.540 #8‐10, 15‐19,23‐26,34

Dec 1­8:40 PM 6