Chapter 6.1 Common Core G.DRT.5 – Use Congruence…criteria 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

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

Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Number of Sides Type 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

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

Polygon Angle-Sum Theorem (n – 2) Polygon Angle-Sum Theorem (n – 2) * 180 where n = the number of sides Corrollary to the Polygon Angle-Sum Theorem The measure of the interior angles of a regular polygon is 𝑛 −2 ∗180 𝑛 Polygon Exterior Angle-Sum Theorem 360° To find one exterior angle of a regular polgon take 360 / n

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

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

If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal, then they cut off congruent segments on every transversal. A B 𝐴 𝐵 = 𝐶 𝐷 C D

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.

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

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

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

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

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

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

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

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

Rectangle Rhombus Square Property Rectangle Rhombus Square 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 ≌

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

Chapter 6.6 Notes Quadrilateral Kite Parallelogram Trapezoid Rhombus Rectangle Isos. Trap. Square

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

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

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

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

Rectangle Rhombus Square Kite Trapezoid Property Rectangle Rhombus Square Kite Trapezoid 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 ≌