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

5.4 You will present 5.4 with your classmates MUST INCLUDE ALL VOCABULARY WORDS You will have all period and 20 minutes tomorrow for your presentation Brainstorm different ideas: PowerPoint Song Poster Notebook in Smartboard Software Game Worksheet YOU WILL BE GRADED FOR THIS ASSIGNMENT!

Presentation 5 Well Spoken and Clearly Organized – Full Participation 4 Organized and Clear – Full Participation 3 Correct information – point came across – mostly everyone participated 2 Some Incorrect information – unorganized – less than half participated 1 Incorrect information – unorganized – unclear – only one person participated Vocabulary Terms 5 Organized, clear, correct All vocabulary terms presented 4 Contains the correct information, few mistakes, organized, all vocabulary words presented 3 Mostly correct, contains some errors, main idea 2 Incorrect information, unorganized, unclear 1 No vocabulary terms Creativity 5 Extreme Creativity! 4 Above Average Creativity 3 Average Creativity 2 Below Average Creativity 1 No Creativity Example Proof5 All information correct 4 Few Errors 3 Average Proof – More than a few mistakes 2 Frequent mistakes 1 No proof

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

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.