Unit 8 Part 3 Properties of Quadrilaterals Trapezoids, Isosceles Trapezoids and Kites

Parts of a Trapezoid

Trapezoid Is a quadrilateral with only one set of parallel sides. (bases) Base1 height Base2

Isosceles Trapezoid Is a quadrilateral with one set of parallel sides and the other two sides are congruent but not parallel.

Isosceles Trapezoid One set of opposite sides are parallel. One set of opposite sides are congruent but not parallel. Base angles are congruent. A Base1 + Base2 angle equal 180° Diagonals are congruent but do not bisect each other.

Parts of an Isosceles Trapezoid

The median of a Trapezoid Median = ½ the sum of the parallel sides. The median is parallel to the other parallel sides.

Example Find the value of ‘x’ if RA is the median. What is the coordinate of point A? (4x-10) (4, 5) F D R A I Y 13 (2, 3) (3x+8)

Example Determine the measure of each angle. m∠1 = 133° m∠2 = 133° 47° 3

Kite Two sets of sides are congruent. The diagonals intersect at 90 degrees and only one of them is bisected. Two sets of congruent triangles are formed by the diagonals.

Kite

Example Calculate the length of AD Given AB = 2x – 3 BC = 5x – 12 DA = x + 2 B A C D

Example Find the measure of ∠1, ∠2, and ∠3 m∠1 = 63° m∠2 = 90° 27° 1 2 34° 3