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.

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Presentation transcript:

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 x + 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.

5.4 Four-Sided Polygons

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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

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

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

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

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.