1. Given: AD is parallel to BC m< D = 8x + 20 m<A = 150 – 6x m<C = 12x + 60 Find x Find m<B Is AB parallel to DC? A C B D <A and <D are supplementary 150 - 6x + 8x +20 = 180 x = 5 m<D = 60 m<A = 120 m<C = 120 Since <D is supplementary to <A, AB is parallel to DC.

2. 5.4 Four-Sided Polygons

3. Polygons: Many sided figures Straight line segments Consecutive sides intersect at endpoints Each vertex belongs to only two sides

4. Name polygons by their sides, either clockwise or counter clock wise. Convex Polygons: A polygon in which each interior angle has a measure less than 180 degrees. yes no

5. Diagonals: a diagonal of a polygon is any segment that connects two non-consecutive (nonadjacent) vertices of a polygon.

6. Formula for diagonals: D = n(n-3) 2 Where n = number of sides

7. Quadrilaterals: 4 sided polygons. Parallelogram: both pairs of opposite sides are parallel Rectangle: at least one right angle Rhombus: at least two consecutive sides are congruent Kite: two disjointed pairs of consecutive sides are congruent Square: parallelogram that is a rectangle and a rhombus

8. Trapezoid: a quadrilateral with exactly one pair of parallel sides. Parallel sides are called the bases of the trapezoid Isosceles trapezoid: trapezoid in which non-parallel sides (legs) are congruent. Base angles are lower and upper base angles.