Download trapezoid

trapezoid
trapezoid
A trapezoid has exactly one pair of
parallel sides.
right trapezoid
A right trapezoid is a trapezoid with two
right angles.
isosceles trapezoid
An isosceles trapezoid is a trapezoid
in which the two sides that are not
parallel are congruent.
isosceles trapezoid
An isosceles trapezoid is a trapezoid
in which the two sides that are not
parallel are congruent.
isosceles trapezoid
An isosceles trapezoid is a trapezoid
in which the two sides that are not
parallel are congruent.
The two congruent sides are called the legs.
The two parallel sides are called the bases.
isosceles trapezoid
B
A
C
D
isosceles trapezoid
C
B
A
E
D
The parallel postulate allows us to
draw a segment (CE) through point
C that is parallel to AB.
isosceles trapezoid
C
B
A
E
D
ABCE is a parallelogram since both
pairs of opposite sides are parallel.
isosceles trapezoid
C
B
A
E
D
AB is congruent to EC, because
opposite sides of a parallelogram are
congruent.
isosceles trapezoid
C
B
A
E
D
EC is congruent to DC, by the
transitive property.
isosceles trapezoid
C
B
A
E
D
Angle CED is congruent to angle D,
because If , then .
isosceles trapezoid
C
B
A
E
D
Angle CED is congruent to angle A,
by corresponding angles.
isosceles trapezoid
C
B
A
E
D
Angle D is congruent to angle A, by
transitive property.
isosceles trapezoid
B
A
C
D
Base angles of an isosceles
trapezoid are congruent.
isosceles trapezoid
B
A
C
D
Angle A and angle B are
supplementary because interior
angles on the same side of a
transversal are supplementary.
Angle C is supplementary to angle
D for same reason.
isosceles trapezoid
B
A
C
D
Angle B is congruent to angle C,
because angles supplementary to
congruent angles are congruent.
isosceles trapezoid
B
A
C
D
AC and DB are the diagonals.
isosceles trapezoid
B
A
C
D
Triangle ABD is congruent to
triangle DCA by SAS.
isosceles trapezoid
B
A
C
D
AC is congruent to DB by CPCTC.
isosceles trapezoid
B
A
C
D
The diagonals of an isosceles
trapezoid are congruent.
Properties of an isosceles trapezoid
B
A
C
D
1. The bases are parallel.
2. The legs are congruent.
3. The lower base angles are congruent.
4. The upper base angles are congruent.
5. The diagonals are congruent.
6. Each lower base angle is supplementary
to each upper base angle.