Post on 18-Dec-2015
Kites, Trapezoids, Midsegments
Geometry Regular ProgramSY 2014-2015
Source:
Discovering Geometry (2008) by Michael Serra
Definitions
Imagine 2 adjacent isosceles triangles.
Kite PropertiesKite Angles Conjecture: The non-vertex angles of a kite are
congruent.
Kite Diagonals Conjecture: The diagonals of a kite are perpendicular.
M
A
T
H
Kite PropertiesKite Angle Bisector Conjecture: The vertex angles of a kite are bisected
by a diagonal.
M
A
T
H
Kite PropertiesKite Diagonal Bisector Conjecture: The diagonal connecting the vertex
angles of a kite is the perpendicular bisector of the other diagonal.
M
A
T
H
Definitions
Trapezoid PropertiesTrapezoid Consecutive Angles
Conjecture: In a trapezoid, the consecutive angles
between the bases are supplementary.
Trapezoid PropertiesIsosceles 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 PropertiesIsosceles Trapezoid Diagonals
Conjecture: In an isosceles trapezoid, the diagonals are
congruent.
Real Life Connection
Real Life Connection
Book Exercises
Book Exercises
p. 271
Answer the following:
Book ExercisesAnswer the following:
p. 271
Book ExercisesAnswer the following:
p. 271
Book ExercisesAnswer the following:
p. 271
Book ExercisesAnswer the following:
p. 271
Book ExercisesAnswer the following:
p. 271
Book ExercisesAnswer the following:
p. 271
Book ExercisesAnswer the following:
p. 271
DefinitionsWhat is a midsegment of a triangle ?
EXAMPLES NON-EXAMPLES
DefinitionsWhat 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.
DefinitionsWhat is a midsegment of a triangle ?
DefinitionsWhat is a midsegment of a trapezoid ?
DefinitionsWhat 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 PropertiesTriangle 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 ExercisesAnswer the following:
p. 277
Book ExercisesAnswer the following:
p. 277
Book ExercisesAnswer the following:
p. 277
Book ExercisesAnswer the following:
p. 277
Book ExercisesAnswer the following:
p. 277
Book ExercisesAnswer the following:
p. 277
Book ExercisesAnswer the following:
p. 277
Book ExercisesAnswer the following:
p. 277
Book ExercisesAnswer the following:
p. 277
MORE ExercisesAnswer the following:
p. 304
MORE ExercisesAnswer the following:
p. 304
MORE ExercisesAnswer the following:
p. 304
MORE ExercisesAnswer the following:
p. 304
MORE ExercisesAnswer the following:
p. 304
MORE ExercisesAnswer the following:
p. 304
MORE ExercisesAnswer the following:
p. 304
MORE ExercisesALWAYS. SOMETIMES. NEVER.
1. The diagonals of a kite are congruent. N
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