Chapter 6 Quadrilaterals Thompson

Special Quadrilaterals Rhombus – four congruent sides Square – four congruent sides and four congruent angles Kite – two pairs of adjacent sides are congruent and no opposite sides are congruent Trapezoid – Exactly one pair of parallel sides Isosceles Trapezoid – the nonparallel sides are congruent. Rectangle – four right angles Parallelogram – both pairs of opposite sides are parallel

Classifying a Quadrilateral Judging by appearance, classify ABCD in as many ways as possible. Quadrilateral and Trapezoid

Relationships Among Special Quadrilaterals Two pairs of parallel sides No parallel sides One pair of parallel sides Parallelogram Kite Trapezoid Rhombus Rectangle Isosceles Trapezoid Square

Using the Properties of Special Quadrilaterals In parallelogram RSTU, m Ð R = 2x – 10 and m Ð S = 3x + 50. Find x.

Closing . . . ABCD is a square. Which classifications from this lesson apply to a square? Which do not apply? A square is: quadrilateral, parallelogram, rectangle, rhombus A square is not: trapezoid, kite

Classifying Quadrilaterals

Directions: When the slide appears say the best name for the quadrilateral aloud. Try to beat the computer by saying the answer before the computer in 4 seconds.

Best Name:

Best Name: Isosceles Trapezoid

Best Name:

Square Best Name: This quadrilateral is also: a rectangle a rhombus a parallelogram

Best Name:

Best Name: Quadrilateral

Best Name:

Best Name: Rhombus This quadrilateral is also: a parallelogram

Best Name:

Best Name: Quadrilateral

Best Name:

Best Name: Rectangle This quadrilateral is also: a parallelogram

Best Name:

Best Name: Isosceles Trapezoid

Best Name:

Rhombus Best Name: This quadrilateral is also: a parallelogram

Best Name:

Best Name: Parallelogram

Best Name:

Best Name: Trapezoid

Best Name:

Best Name: Quadrilateral

Best Name:

Best Name: Parallelogram

Best Name:

Best Name: Trapezoid

Best Name:

Best Name: Rectangle This quadrilateral is also: a parallelogram

Best Name:

Best Name: Rhombus This quadrilateral is also: a parallelogram

Best Name:

Square Best Name: This quadrilateral is also: a rectangle a rhombus a parallelogram

Best Name:

2nd Stellation Of Icosododecahedron

Game Over!

Classwork Page 290 #’s 1-12, 19, 22, 23, 29-34, 37-42, 55

Properties of Parallelograms Lesson 6-2

Key to remembering these! We’re going to be learning a lot of similar looking theorems. Draw a few pictures to see what happens.

Thm 6-1 Opposite sides of a parallelogram are congruent. Other Properties of Parallelograms: Opposite sides are parallel Consecutive angles are supplementary

Using Consecutive Angles Use parallelogram KMOQ to find m Ð O. m Ð O = 145

Thm 6-2 Opposite angles of a parallelogram are congruent.

Thm 6-3 The diagonals of a parallelogram bisect each other.

Using Thms. 6-1 and 6-2 Find the value of x in parallelogram ABCD. Then find m Ð A. m Ð A = 105

Example 1 Find the values of x and y.

Example 2 Find each indicated measure. NM KM mJKL mLKM

Thm 6-4 If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Proving That a Quadrilateral is a Parallelogram Lesson 6-3

Thm 6-5 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Thm 6-6 If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

Finding Values for Parallelograms Find values of x and y for which ABCD must be a parallelogram. x = 18 and y = 89

Thm 6-7 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Thm 6-8 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Is the Quadrilateral a Parallelogram? Determine whether the quadrilateral is a parallelogram. Explain.

Classwork Page 297 #’s 18, 20, 40, 43, 46, 47 Page 307 #’s 7-15, 32-34