5.3 Kite and Trapezoid Properties

Objectives:•Discover properties of kites and trapezoids•Lear new vocabulary•Practice Construction skills

Investigation 1:What are some properties of kites?

• Using patty paper, follow the directions on p.266.

• Are the vertex angles congruent? ___________

• Are the nonvertex angles congruent? _____________

Kite Angles Conjecture The _____________ angles of a kite are ________________

no

yes

nonvertex congruent

• Step 3How are the diagonals related? ________________________

Kite Diagonals Conjecture The diagonals of a kite are ______________________________

• Step 4Does either diagonal bisect each other? ___________________________Kite Diagonal Bisector ConjectureThe diagonal connecting the vertex angles of a kite is the

___________________ of the other diagonal.

• Step 5Does either diagonal bisect any angles? ___________________________Kite Angle Bisector Conjecture

The ________________angles of a kite are ___________ by a

_________________.

perpendicular

perpendicular

yes

Perpendicular bisector

yes

vertex bisected

diagonal

Investigation 2: What are some properties of trapezoids• Follow the steps on p.268. What do you notice about the sum of the measures of each pair of consecutive angles between the parallel bases? _______________________________________

Trapezoid Consecutive Angles Conjecture The consecutive angles between the bases of a trapezoid are _________________ • Follow steps 4 and 5 on p.269 What do you notice about the pair of base angles in each trapezoid? _____________

Isosceles Trapezoid Conjecture The base angles of an isosceles trapezoid are _________________________ •Step 7 Draw both diagonals. Compare the lengths. __________________________

Isosceles Trapezoid Diagonals ConjectureThe diagonals of an isosceles trapezoid are ________________________

Add up to 180

supplementary

The same

congruent

The same

congruent