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Chapter 6.1 Common Core G.DRT.5 Use Congruencecriteria to solve problems and prove relationships in geometric figures. Objectives To find the sum of the measures of the interior and exterior angles of a polygon

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Chapter 6.1 Notes Polygon is a simple, closed figure made with straight lines. vertex vertex side side Convex has no indentation Concave has an indentation

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Number of SidesType of Polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 11 Unadecagon 12 Dodecagon n n - gon

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Equilateral Equiangular Regular Diagonal Interior Angles of a Quadrilateral sum of the interior angles of any Quad. is _ _ _.

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Chapter 6.2 Common Core G.CO.11 & G.SRT.5 - Prove theorems about parallelograms. Objectives To use relationships among sides, angles, & diagonals of parallelograms

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Chapter 6.2 Notes Thm Opposite sides are in a parallelogram Thm Opposite s are in a parallelogram Thm Consecutive s are supp. in a parallelogram Thm Diagonals bisect each other in a parallelogram

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Chapter 6.3 Common Core G.CO.11 & G.SRT.5 - Prove theorems about parallelograms.the diagonals of a parallelogram bisect each other and its converses Objectives To determine whether a quadrilateral is a parallelogram.

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Chapter 6.3 Notes The five ways of proving a quadrilateral is a parallelogram. (p.371) 1) 2) 3) 4) 5)

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Chapter 6.4 Common Core G.CO.11 & G.SRT.5 Prove theorems about parallelogramsrectangles are parallelograms with congruent diagonals. Objectives To define and classify special types of parallelograms. To use properties of diagonals of rhombuses and rectangles.

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Chapter 6.4 Parallelogram Quad. with 2 sets of parallel sides Rhombus is a parallelogram with 4 sides Rectangle is a parallelogram with 4 rt. angles Square - is a parallelogram with 4 sides and four right angles

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Thm a parallelogram is a rhombus if and only if its diagonal are perpendicular Thm a parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles Thm - a parallelogram is a rectangle if and only if its diagonals are congruent

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Chapter 6.5 Common Core G.CO.11 & G.SRT.5 Prove theorems about parallelogramsrectangles are parallelograms with congruent diagonals. Objective To determine whether a parallelogram is a rhombus or rectangle.

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Chapter 6.5 Parallelogram Quad. with 2 sets of parallel sides Rhombus is a parallelogram with 4 sides Rectangle is a parallelogram with 4 rt. Angles Square - is a parallelogram with 4 sides and four right angles

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Ways to prove a Quad. is a Rhombus 1) Prove it is a parallelogram with 4 sides 2) Prove the quad. is a parallelogram and then show diagonals are perpendicular 3) Prove the quad. is a parallelogram and then show that the diagonals bisect the opposite angles

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Way to Prove a parallelogram is a Rectangle If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

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PropertyRectangleRhombusSquare Both pairs of opp. sides are II Exactly 1 pair of opp. sides are II All s are Diagonals are Diagonals are Diagonals bisect each other Both pairs of opp. Sides are Exactly 1 pair of opp. sides are All sides are

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Chapter 6.6 Common Core G.SRT.5 Use congruencecriteria to solve problems and prove relationships in geometric figures. Objective To verify and use properties of trapezoids and kites

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Chapter 6.6 Notes Quadrilateral KiteParallelogramTrapezoid Rhombus RectangleIsos. Trap. Square

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Trapezoid is a quadrilateral with exactly one pair of parallel sides. Isosceles Trapezoid is a trapezoid with congruent legs

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Thm If a trapezoid is isosceles, then each pair of base angles is congruent Thm If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. Thm a trapezoid is isosceles if and only if its diagonals are congruent

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Midsegment Thm for Trapezoids the midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases

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Thm If a quadrilateral is a kite, then its diagonals are perpendicular. Thm - If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent

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PropertyRectangleRhombusSquareKiteTrapezoid Both pairs of opp. sides are II Exactly 1 pair of opp. sides are II All s are Diagonals are Diagonals are Diagonals bisect each other Both pairs of opp. Sides are Exactly 1 pair of opp. sides are All sides are