Lesson 6-1. Warm-up Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√3.

QuadrilateralsLesson 6-1

Warm-up

Warm-upSolve the following triangles using the

Pythagorean Theorem a2 + b2 = c2

95

12 9

8

8√3

Warm-upFind the missing point given the following

information.

1. Point 1 (3, 8), Point 2 (5, 12), Midpoint (x, y)

2. Point 1 (-2, 5), Point 2 (3, -3), Midpoint (x, y)

3. Point 1 (2, 4), Point 2 (x, y), Midpoint (5, -1)

4. Point 1 (-1, 2), Point 2 (2, y), distance = 5

ParallelogramsA parallelogram is a quadrilateral with both

pairs of opposite sides parallel

Properties of ParallelogramsIts opposite sides are congruentIts opposite angles are congruentIts consecutive angles are supplementary

(add to 180°)Its diagonals bisect each other. (Cut each

other into 2 equal sections)

Let’s PracticeFind the value of each variable in the

parallelogram.

Let’s PracticeFind the value of each variable in the

parallelogram.

Types of ParallelogramsRhombus – a parallelogram with four congruent

sides.Rectangle – a parallelogram with four right angles.Square – a parallelogram four congruent sides and

four right angles.Rhombus Corollary – a quadrilateral is a rhombus

if and only if it has four congruent sides.Rectangle Corollary – a quadrilateral is a

rectangle if and only if it has four right angles.Square Corollary – a quadrilateral is a square if

and only if it is a rhombus and a rectangle.

Special Parallelogram PropertiesIf a parallelogram is a rhombus, its diagonals

are perpendicular.

If a parallelogram is a rhombus, each diagonal bisects a pair of opposite angles.

If a parallelogram is a rectangle, its diagonals are congruent.

Let’s PracticeClassify the special quadrilateral. Explain

your reasoning. Then find the values of x and y.

Let’s PracticeClassify the special quadrilateral. Explain

your reasoning. Then find the values of x and y.

Other QuadrilateralsTrapezoid – a quadrilateral with exactly one

pair of parallel sides.

Kite – a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

Trapezoid VocabularyBase - the parallel sides are the bases.Base Angles - in a trapezoid, the two angles

that have that base as a side.Legs – the non-parallel sides of a trapezoid.Isosceles Trapezoid – a trapezoid where

both legs are congruent.Midsegment of a Trapezoid – the segment

that connects the midpoints of the legs of a trapezoid.

Trapezoid Properties For an isosceles trapezoid, each pair of base

angles is congruent.For an isosceles trapezoid, the diagonals are

congruent.Midsegment Theorem 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.

Kite PropertiesIts diagonals are perpendicularExactly one pair of opposite angles are

congruent.The diagonal between the non-congruent

angles bisects the diagonal between the congruent angles.

Let’s PracticeFind “x”.

Let’s Practice

Let’s Practice