Geometry Quick Discussion 10.1 Squares and Rectangles 10.2 Parallelograms and Rhombi 10.3 Kites and Trapezoids

Objectives 10.1-10.3 Determine the properties of squares and rectangles Determine the properties of parallelograms and rhombi Determine the properties of kites and trapezoids

Properties of Quadrilaterals Fill in the form as we go Sides Angles Diagonals Other

10.1 Properties of Squares and Rectangles Properties of a Square All sides congruent All angles are congruent All angles are right angles Opposite sides are parallel Diagonals are congruent Diagonals bisect each other The vertex angles are bisected by the diagonals The diagonals are perpendicular

10.1 Properties of Squares and Rectangles Properties of a Rectangle Opposite sides are congruent All angles are right angles All angles are congruent Opposite sides are parallel Diagonals are congruent The diagonals bisect each other

10.2 Properties of Parallelograms and Rhombi Parallelogram/Congruent-Parallel Side Theorem (Page 761) If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram. Properties of a Parallelogram Opposite sides are congruent Opposite sides are parallel Opposite angles are congruent The diagonals are bisected

10.2 Properties of Parallelograms and Rhombi Properties of a Rhombus All sides are congruent Opposite angles are congruent Opposite sides are parallel The diagonals are perpendicular The diagonals bisect each other The angles are bisected by the diagonals

10.3 Properties of Kites and Trapezoids Properties of a Kite Two disjoint pairs of consecutive sides congruent 2 different sets of consecutive sides congruent Non-vertex angles are congruent Angles between the non-congruent sides The diagonals are perpendicular The diagonal connecting the congruent angles is bisected by the other diagonal The vertex angles are bisected by the diagonal

10.3 Properties of Kites and Trapezoids Properties of a Trapezoid One set of sides are parallel (bases) In an isosceles trapezoid, the non-parallel sides are congruent In an isosceles trapezoid, the base angles are congruent Angles on each side of the bases

10.3 Problem 4: Midsegment of a Trapezoid Collaborate 1-8 (10 Minutes) Pg. 781 (-4,4) (2,4) (-7,-5) (7,-5)

10.3 Problem 4: Midsegment of a Trapezoid

10.3 Problem 4: Midsegment of a Trapezoid The midsegment of a trapezoid is formed by connecting the midpoints of the legs of the trapezoid.

10.3 Problem 4: Midsegment of a Trapezoid

10.3 Problem 4: Midsegment of a Trapezoid

10.3 Problem 4: Midsegment of a Trapezoid The Trapezoid Midsegment Theorem The midsegment of a trapezoid is parallel to each of the bases and its length is one half the sum of the lengths of the bases. 𝑀𝐺 ∥ 𝐽𝐸 ∥ 𝐷𝑆 𝐽𝐸= 1 2 (𝑀𝐺+𝐷𝑆)

Formative Assessment Skills Practice 10.1 Skills Practice 10.2 Pg. 714-715 (7-18) Skills Practice 10.2 Pg. 723-724 (1-8) Skills Practice 10.3 Vocab Pg. 733 (1-4) Problems Pg. 733-734 (1-8), Pg. 737-740 (15-26)