Kites and Trapezoids - PowerPoint Presentation

Slide1

Kites and TrapezoidsSlide2

ReviewSlide3

Interior Angles in a Polygon

The sum of the angles of the interior angles of a convex n-gon is (n-2)

•

180

°

An angle in a regular polygon is

(n-2)

•

180

°/nSlide4

Exterior Angle Theorem

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360

°Slide5

Exterior Angle Theorem

The measure of each exterior angle of a regular n-gon is 360°/nSlide6

New MaterialSlide7

Lesson Objectives:

By the end of class tomorrow, you will…..

Discover properties of kites and trapezoids.

Learn new vocabulary.

Practice construction skills.Slide8

Kite Investigation

Recall the shape of a toy kite. What definition would you write to describe the shape in geometric terms?Slide9

Kite Investigation

Kite Definition

A

kite

is a quadrilateral that has two pairs of consecutive congruent sides, but the opposite sides are not congruentSlide10

Kite Investigation

Get your supplies

Straight Edge

Patty PaperSlide11

Kite Investigation

On a piece of patty paper, draw two line segments of different lengthSlide12

Kite Investigation

Fold the paper, so that the endpoints are exactly on the foldSlide13

Kite Investigation

Trace the first two segments through the patty paperSlide14

Kite Investigation

Unfold the paper and label your kite G,L,A,D

G

L

A

DSlide15

Kite Investigation

Measure each of the four angles

What conclusions can you draw?

G

L

A

DSlide16

Kite Angles Conjecture

The non-vertex angles of a kite are congruentSlide17

Kite Investigation

Add the diagonals into your diagram

Label the intersecting point M

G

L

A

D

MSlide18

Kite Investigation

Measure the angles at point M

What can you conclude about the diagonals?

G

L

A

D

MSlide19

Kite Diagonals Conjecture

The diagonals of a kite are perpendicularSlide20

Kite Investigation

Measure LM and MD

What can you conclude?

G

L

A

D

MSlide21

Kite Diagonal Bisector Conjecture

The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonalSlide22

Kite Investigation

Fold along the diagonals

Does either diagonal bisect any angles?

G

L

A

D

MSlide23

Kite Angle Bisector Conjecture

The vertex angles of a kite are bisected by a diagonalSlide24

Trapezoid Definition

Trapezoid Definition

A

trapezoid

is a quadrilateral with exactly one pair of parallel sidesSlide25

Trapezoid Vocabulary

Trapezoid Definitions

The parallel sides are called

bases

A pair of angles that share a base are called

base angles

A&B, C&D

A

B

C

DSlide26

Trapezoid Consecutive Angles Conjecture

The consecutive angles between the bases of a trapezoid are supplementarySlide27

Trapezoid Investigation

Isosceles Trapezoid

An

isosceles trapezoid

has congruent legs

A

B

C

DSlide28

Trapezoid Investigation

Get your supplies

Protractor

Straight Edge

PaperSlide29

Trapezoid Investigation

Draw two parallel lines –

at least two inches apart

Use a compass to create two equal length legs

Label the vertices H,O,W,E

H

O

W

ESlide30

Trapezoid Investigation

Measure each pair of base angles

H

O

W

E

angle

H

= ?

angle O = ?

angle W = ?

angle E = ?Slide31

Trapezoid Investigation

What can you conclude about the base angles in an isosceles trapezoid?

H

O

W

ESlide32

Isosceles Trapezoid Conjecture

The base angles of an isosceles trapezoid are congruentSlide33

Trapezoid Investigation

Add the diagonals of the isosceles trapezoid

H

O

W

ESlide34

Trapezoid Investigation

Compare the lengths of the two diagonals

What conclusion can we make?

H

O

W

ESlide35

Isosceles Trapezoid Diagonals Conjecture

The diagonals of an isosceles trapezoid are congruentSlide36

Practice ProblemsSlide37
Slide38

53

°

127

°

127

°Slide39

DF=10

Angle C=85°

Angle

D=95°

Angle F=85°Slide40

a = 129.5

°

h

= 129.5

°Slide41

a = 118

°

t

= 43

°Slide42

90

°

48

°Slide43

Homework

5.3 Worksheet