Week 14 day 4

6

The sums of the angle measures of three polygons are given. Based on the pattern, what will be the sum of the measures of a hexagon in degrees?

Record your answer and be sure to use the correct place value.

180° 360° 540°•

6.5 Trapezoids 6.5 Trapezoids and Kitesand Kites

PardekooperPardekooper

1st, lets look at some theorems

• The base angles of an The base angles of an isosceles trapezoid are isosceles trapezoid are

congruent.congruent.

PardekooperPardekooper

1st, lets look at some theorems

• The diagonals of an The diagonals of an isosceles trapezoid are isosceles trapezoid are

congruent.congruent.A B

CD

AC BD

PardekooperPardekooper

1st, lets look at some theorems

• The diagonals of a kite The diagonals of a kite are perpendicular.are perpendicular.

• One of the diagonals is One of the diagonals is an angle bisectoran angle bisector

• One pair of angles One pair of angles are congruentare congruent

PardekooperPardekooper

OK, here comes a problem.OK, here comes a problem.The following is an isosceles trapezoid. Find The following is an isosceles trapezoid. Find

the measure of the numbered angles.the measure of the numbered angles.

2 3

1650

1 = 651 = 6500

656500++1+1+2+2+3 = 3603 = 36000

656500+ 65+ 6500+x+x = 360+x+x = 36000

13013000+x+x = 360+x+x = 36000

13013000+2x = 360+2x = 36000

-130-1300 0 -130-13000

2x = 2302x = 23000

2 22 2x = 115x = 11500

3 = 1153 = 11500

2 = 1152 = 11500

The sum of the angles of a

quadrilateral is 3600

Remember 2 3

PardekooperPardekooper

How about another problem.How about another problem.Find the measure of the numbered angles in Find the measure of the numbered angles in

the kite.the kite.2 = 902 = 9000

3 = 903 = 9000

454500+ 90+ 9000++1 = 1801 = 18000

13513500+x = 180+x = 18000

-135-1350 0 -135-13500

x = 45x = 4500

1 = 451 = 4500

2 13

450

diagonals of a kite

are perpendicular

Remember The sums of the angles

of a triangle equals 1800

PardekooperPardekooper

Here comes the assignment.Here comes the assignment.PardekooperPardekooper

AssignmentWorkbook

Page 365 all