Bellwork  Solve for x x-2 5x-13 No Clickers

Bellwork Solution  Solve for x x-2 5x-13

Bellwork Solution  Solve for x

Bellwork Solution  Solve for x

Section 8.5

The Concept  In this chapter we’ve talked about polygons, quadrilaterals, parallelograms, rhombuses, rectangles and squares  Today we’re going to add to our list of special quadrilaterals Quadrilaterals Polygons Parallelograms Rhombuses Rectangles Squares Trapezoids Kites

Trapezoids Defined Trapezoid Quadrilateral with exactly one pair of parallel sides called bases Each Trapezoid has two pairs of base angles Pair #1 Pair #2 A trapezoid is not a parallelogram because only one set of opposite sides are parallel Legs This means that the only way to prove a quadrilateral is a trapezoid is by proving that two sides are parallel

Proving via Coordinates Is the quadrilateral with vertices A(-5,0), B(2,3), C(3,1), D(-2,-2) a trapezoid? Proving parallelism is done by looking at the slopes of the two lines and determining if they are equal

IsoscelesTrapezoids Isosceles Trapezoid Trapezoid with congruent legs

Theorems Theorem 8.14: If a trapezoid is isosceles, then each pair of base angles is congruent Theorem 8.15: If a trapezoid has a pair of congruent base angles then it is an isosceles trapezoid Theorem 8.16 A trapezoid is isosceles if and only if its diagonals are congruent

Right Trapezoids Right Trapezoid Trapezoid with two interior right angles

Midsegments If we remember from Chapter 5, a midsegment is a segment that connects the midpoints of opposite sides In Chapter 5, we found that these segments are parallel to the bases of the triangles in which they are drawn. We find the same applies in trapezoids We also find this theorem Theorem 8.17: The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases

Example Find the length of the midsegment AB AB 15 13

Example If AB is a midsegment, solve for x AB 2x+4 2x

Kites We discussed the concept of kites in chapter 11, but let’s formally define them Kite Quadrilateral with two pairs of consecutive congruent sides, but opposite sides are not congruent

Theorems Theorem 8.18: If a quadrilateral is a kite, then its diagonals are perpendicular Theorem 8.19: If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent Only these two

Example Find the measure of the missing angles 110 o B 15 A 20 o

Homework  8.5 1, 2-30 even, 34-36

Most Important Points  Trapezoids  Properties of Isosceles Trapezoids  Kites