1. Understand, use and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.
MM1G3d

2. Vocabulary
Trapezoid: a quadrilateral with exactly one pair of parallel sides.
The parallel sides are the bases. A B
bases D C

3. 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

4. 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

5. 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

6. Theorem
If a trapezoid is isosceles, then each pair of base angles is congruent.
<A is congruent to <B.
<C is congruent to <D. A B D C

7. Theorem
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. A B D C

8. 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

9. 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

10. Example 1
Find the missing angle measures for the isosceles trapezoid ABCD.
<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
x + x = 360
2x +184 = 360
– 184 – 184
2x = 176 A B
92°
92° x x C D

11. Example 1
Find the missing angle measures for the isosceles trapezoid ABCD.
<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
x + x = 360
2x +184 = 360
– 184 – 184
2x = 176
x = 88 A B
92°
92°
88°
88° C D

12. Example 2 EF is the midsegment of trapezoid ABCD. Find x. x = 12 + 20

13. Example 3 EF is the midsegment of trapezoid ABCD. Find x. 2 *
– – 16
x = 18
* 2 A x B 17 E F D C 16

14. Vocabulary
kite: a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

15. Theorem
If a quadrilateral is a kite, then its diagonals are perpendicular.

16. Theorem
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

17. Example 4 EFGH is a kite. Find m<F. E
In a kite, one pair of opposite
angles is congruent.
Therefore, <H is congruent to <F.
So, m<F = 83°.
124° H
83° F G

18. Assignment
Textbook: p (1-14) & p331 (1-6)