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Kites, Trapezoids,
Midsegments
Geometry
Regular Program
SY 2014-2015
Source:
Discovering Geometry (2008) by Michael Serra
Definitions
Imagine 2 adjacent isosceles triangles.
Kite Properties
Kite Angles Conjecture:
The non-vertex angles of a kite are congruent.
Kite Diagonals Conjecture:
The diagonals of a kite are perpendicular.
A
M
T
H
Kite Properties
Kite Angle Bisector Conjecture:
The vertex angles of a kite are bisected by a
diagonal.
A
M
T
H
Kite Properties
Kite Diagonal Bisector Conjecture:
The diagonal connecting the vertex angles of
a kite is the perpendicular bisector of the
other diagonal.
A
M
T
H
Definitions
Trapezoid Properties
Trapezoid Consecutive Angles Conjecture:
In a trapezoid, the consecutive angles
between the bases are supplementary.
Trapezoid Properties
Isosceles Trapezoid Conjecture:
In an isosceles trapezoid, the base angles are
congruent.
*Converse of Isosceles Trapezoid Conjecture:
In a trapezoid, if the base angles are
congruent, then the trapezoid is isosceles.
Trapezoid Properties
Isosceles Trapezoid Diagonals Conjecture:
In an isosceles trapezoid, the diagonals are
congruent.
Real Life Connection
Real Life Connection
Book Exercises
Book Exercises
Answer the following:
p. 271
Book Exercises
Answer the following:
p. 271
Book Exercises
Answer the following:
p. 271
Book Exercises
Answer the following:
p. 271
Book Exercises
Answer the following:
p. 271
Book Exercises
Answer the following:
p. 271
Book Exercises
Answer the following:
p. 271
Book Exercises
Answer the following:
p. 271
Book Exercises
Answer the following:
p. 271
Definitions
What is a midsegment of a triangle ?
EXAMPLES
NON-EXAMPLES
Definitions
What is a midsegment of a triangle ?
A midsegment of a triangle is…
a segment whose endpoints are the
midpoints of two sides of a triangle.
Definitions
What is a midsegment of a triangle ?
Definitions
What is a midsegment of a trapezoid ?
Definitions
What is a midsegment of a trapezoid ?
A midsegment of a trapezoid is…
a segment whose endpoints are the
midpoints of the non-parallel sides (legs) of
a trapezoid.
Can you draw non-examples of a
midsegment of a trapezoid?
Midsegment Properties
Triangle Midsegment Conjecture:
In a triangle, the midsegment is parallel to the
third side, and measures half the length of
the third side.
Trapezoid Midsegment Conjecture:
In a trapezoid, the midsegment is parallel to
the bases, and measures half the sum of the
lengths of the bases.
Book Exercises
Answer the following:
p. 277
Book Exercises
Answer the following:
p. 277
Book Exercises
Answer the following:
p. 277
Book Exercises
Answer the following:
p. 277
Book Exercises
Answer the following:
p. 277
Book Exercises
Answer the following:
p. 277
Book Exercises
Answer the following:
p. 277
Book Exercises
Answer the following:
p. 277
Book Exercises
Answer the following:
p. 277
Exercises
Answer the following:
p. 304
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Exercises
Answer the following:
p. 304
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Exercises
Answer the following:
p. 304
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Exercises
Answer the following:
p. 304
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Exercises
Answer the following:
p. 304
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Exercises
Answer the following:
p. 304
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Exercises
Answer the following:
p. 304
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Exercises
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ALWAYS. SOMETIMES. NEVER.
1. The diagonals of a kite are congruent.
S
2. Consecutive angles of a kite are supplementary. N
3. The diagonal connecting the vertex angles of a kite
divides the kite into two congruent triangles.
A
4. The diagonals of a trapezoid bisect each other. N
5. The three midsegments of a triangle divide the
triangle into 4 congruent triangles. A
6. The midsegment of a trapezoid is perpendicular to a
leg of the trapezoid. S