Download G_PP_6-5_TrapezoidsKites

Trapezoids and Kites
Geometry 6-5
Recall the shape of a toy kite.
What definition would you write
to describe the shape in
geometric terms?
Kite Investigation
Kite Definition
• A kite is a quadrilateral that has
two pairs of consecutive
congruent sides, but the
opposite sides are not congruent
Kite Investigation
• Get your supplies
–Straight Edge
–Patty Paper
Kite Investigation
• On a piece of patty paper, draw
two line segments of different
length
Kite Investigation
• Fold the paper, so that the
endpoints are exactly on the fold
Kite Investigation
• Trace the first two segments
through the patty paper
Kite Investigation
• Unfold the paper and label your kite
G,L,A,D
L
G
A
D
Kite Investigation
• Measure each of the four angles
• What conclusions can you draw?
L
G
A
D
Kite Investigation
• The non-vertex angles of a
kite are congruent
Kite Angles Conjecture
• Add the diagonals into your diagram
• Label the intersecting point M
L
G
M
A
D
Kite Investigation
• Measure the angles at point M
• What can you conclude about the
diagonals?
L
G
M
A
D
Kite Investigation
• The diagonals of a kite are
perpendicular
Kite Diagonals Conjecture
• Measure LM and MD
• What can you conclude?
L
G
M
A
D
Kite Investigation
• The diagonal connecting the
vertex angles of a kite is the
perpendicular bisector of the
other diagonal
Kite Diagonal Bisector Conjecture
• Fold along the diagonals
• Does either diagonal bisect any angles?
L
G
M
A
D
Kite Investigation
• The vertex angles of a kite
are bisected by a diagonal
Kite Angle Bisector Theorem
Trapezoid Definition
• A trapezoid is a quadrilateral with exactly
one pair of parallel sides
Trapezoid Definition
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
C
B
D
Trapezoid Vocabulary
• The consecutive angles between the
bases of a trapezoid are supplementary
Trapezoid Consecutive Angles
Theorem
Isosceles Trapezoid
• An isosceles trapezoid has congruent
legs
A
C
B
D
Trapezoid Investigation
• Get your supplies
– Protractor
– Straight Edge
– Paper
Trapezoid Investigation
• Draw two parallel lines – at least two inches apart
• Use a compass to create two equal
length legs
• Label the vertices L,I,O,N
L
O
I
N
Trapezoid Investigation
• Measure each pair of base angles
angle L = ?
angle I = ?
L
O
I
angle O= ?
angle N = ?
N
Trapezoid Investigation
• What can you conclude about the base
angles in an isosceles trapezoid?
L
O
I
N
Trapezoid Investigation
The base angles of an isosceles
trapezoid are congruent
Isosceles Trapezoid Theorem
• Add the diagonals of the isosceles
trapezoid
L
O
I
N
Trapezoid Investigation
• Compare the lengths of the two diagonals
• What conclusion can we make?
L
O
I
N
Trapezoid Investigation
• The diagonals of an isosceles
trapezoid are congruent
Isosceles Trapezoid Diagonals
Practice Problems
53°
127°
127°
Practice Problems
•DF=10
•Angle C=85°
•Angle D=95°
•Angle F=85°
Practice Problems
a = 129.5°
h = 129.5°
Practice Problems
a = 118°
t = 43°
Practice Problems
90°
48°
Practice Problems
• Pages 322 – 325
• 2-16 even, 22-24, 27,28,32-37,
56
Homework