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Transcript
6.2 Parallelograms Check.3.2 , Connect coordinate geometry to geometric figures in the plane (e.g. midpoints, distance formula, slope, and polygons). Check.4.10 , Identify and apply properties and relationships of special figures (e.g., isosceles and equilateral triangles, family of quadrilaterals, polygons, and solids). Spi.3.2 Use coordinate geometry to prove characteristics of polygonal figures. Copy the following into your notes: Parallelograms A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A B C D Properties of Parallelogram Opposite Sides of a parallelogram are congruent Opposite Angles of a parallelogram are congruent Consecutive Angles of a parallelogram are supplementary. mA+ mB = 180, mB+ mC = 180 mC+ mD = 180, mD+ mA = 180 If a parallelogram has 1 right angle, it has 4 right angles Objective: To understand and be able to apply properties of sides, angles and diagonals of parallelograms. Parallelograms A parallelogram is a quadrilateral with both pairs of opposite sides parallel. B A C D Properties of Parallelogram Diagonals of a parallelogram bisect each other Each Diagonal of a parallelogram separates the parallelogram in to two congruent Triangles Applying Properties • Quadrilateral LMNP is a parallelogram. – Find mPLM, mLMN, and d. • • • • mPNM = 66 + 42 = 108 by angle addition mPNM = mPLM Opposite angles of parallelogram are mPLM = 108 Substitution mPL M + mLMN = 180, Consecutive Angles of parallelograms are supplementary. • 108 + mLMN = 180, substitution • mLMN = 72 • LM PN, opposite sides of Parallelogram are congruent • 2d = 22 • D = 11 Solve 3y = 18 y=6 URT = 40 UTS = 18+40 = 58 UTS = URS = 58 UTS + RST = 180 58 + RST = 180 RST = 122 Diagonals of Parallelogram • What are the coordinates of the intersection of the diagonals of a parallelogram ABCD with vertices A(2, 5), B(6,6), C(4,0) and D(0, -1)? • Diagonals of parallelogram bisect each other. Summary • Parallelograms have – Opposite sides are parallel and congruent – Opposite angles are congruent – Consecutive angles are supplementary – Diagonals bisect each other • Practice Assignment • Block Page 404, 10 - 22 Even