Transcript MM1G3d - PBworks

Understand, use and prove properties of and
relationships among special quadrilaterals:
parallelogram, rectangle, rhombus, square, trapezoid,
and kite.
Vocabulary

Trapezoid: a quadrilateral with exactly
one pair of parallel sides.
 The parallel sides are the bases.
A
B
bases
D
C
Vocabulary

Trapezoid: a quadrilateral with exactly
one pair of parallel sides.
 The parallel sides are the bases.
 For each of the bases of a trapezoid, there
is a pair of base angles, which are the two
angles that have that base as a side.
A
B
base angles
D
C
Vocabulary

Trapezoid: a quadrilateral with exactly
one pair of parallel sides.
 The nonparallel sides of a trapezoid are the
legs of the trapezoid.
 If the legs of a trapezoid are congruent, then
the trapezoid is an isosceles trapezoid.
A
B
legs
D
C
Vocabulary

Trapezoid: a quadrilateral with exactly
one pair of parallel sides.
 The midsegment of a trapezoid is the
segment that connects the midpoints of its
legs.
A
B
midsegment
D
C
Theorem

If a trapezoid is isosceles, then each
pair of base angles is congruent.
A
D
<A is congruent to <B.
<C is congruent to <D.
B
C
Theorem

If a trapezoid has a pair of congruent
base angles, then it is an isosceles
trapezoid.
A
D
B
C
Theorem

A trapezoid is isosceles if and only if its
diagonals are congruent.
A
B
AC is congruent to BD, so ABCD
is an isosceles trapezoid.
D
C
Midsegment Theorem for
Trapezoids

The midsegment of a trapezoid is
parallel to each base and its length is
one half the sum of the lengths of the
bases.
A
B
x = AB + CD
2
x
D
C
Example 1

Find the missing angle measures for the
isosceles trapezoid ABCD.
A
B
92°
x
D
<A and <B are base angles, so
they are congruent.
m<B = 92
ABCD is a quadrilateral so the
angles add up to 360°.
<C and <D are base angles, so
they are congruent.
92°
x
C
x + x + 92 + 92 = 360
2x +184 = 360
– 184 – 184
2x = 176
2
2
Example 1

Find the missing angle measures for the
isosceles trapezoid ABCD.
A
B
92°
88°
D
<A and <B are base angles, so
they are congruent.
m<B = 92
ABCD is a quadrilateral so the
angles add up to 360°.
<C and <D are base angles, so
they are congruent.
92°
88°
C
x + x + 92 + 92 = 360
2x +184 = 360
– 184 – 184
2x = 176
2
2
x = 88
Example 2

A
EF is the midsegment of trapezoid
ABCD. Find x.
12
x = 12 + 20
2
x = 32
2
x = 16
B
x
E
D
F
20
C
Example 3

A
EF is the midsegment of trapezoid
ABCD. Find x.
x
2 *17 = x + 16 * 2
2
34 = x + 16
– 16
– 16
B
17
E
D
x = 18
F
16
C
Vocabulary

kite: a quadrilateral that has two pairs of
consecutive congruent sides, but
opposite sides are not congruent.
Theorem

If a quadrilateral is a kite, then its
diagonals are perpendicular.
Theorem

If a quadrilateral is a kite, then exactly
one pair of opposite angles are
congruent.
Example 4

EFGH is a kite. Find m<F.
E
124°
H
83°
F
G
In a kite, one pair of opposite
angles is congruent.
Therefore, <H is congruent to <F.
So, m<F = 83°.
Assignment

Textbook: p.325-326 (1-14) & p331 (1-6)