/Geo_Sec._8.5

Geometry Chapter 8 - Polygons and Quadrilaterals Section 8.5 - Use Properties of Kites and Trapezoids

What the student should get from this: !" Use properties of kites to solve problems #" Use properties of trapezoids to solve problems Let’s look again at the family tree for quadrilaterals.

Quadrilaterals

Trapezoids

Parallelograms

Kites Rectangles

Rhombuses

Squares What is a kite? It is a quadrilateral with exactly two pairs of ________________ __________________ sides.

Draw a kite. Show that it is a kite.

Some properties you need to know about kites: 1. Exactly one pair of opposite angles are congruent 2. The diagonals are at right angles to each other Example: for kite ABCD, show the angles that are congruent. Indicate their measures if possible.

B A

C D

P Given: kite SPQR with Prove: Statements

and

.

S

Reasons

Q R

y

a kite

5 cm

Example: solve for the variables z

12 cm

30 cm x

Lastly... a trapezoid is a quadrilateral with only one pair of congruent opposite sides.

Draw and label the parts of a trapezoid.

Some properties you need to know about trapezoids: 1. The parallel sides are called bases 2. In an isosceles trapezoid, the opposite angles are congruent 3. In an isosceles trapezoid, base angles are congruent 4. In an isosceles trapezoid, the diagonals are congruent Example: for isosceles trapezoid ABCD, find the measures of the missing angles.

B

A

C

78Ëš

D Find the value of x so that the trapezoid is isosceles.

Also... the median of a trapezoid is always found by adding the length of the bases and dividing by two.

Example: solve for the length of the median in trap ABCD.

Solve for x.

25

43

42

66

Assignment: p.546 #s 7-15 all, 18-27 all - due next class. One class period late will be 50% off. Beyond that, no credit given. Show work and draw all the pictures.