5. Vocabulary
1.Trapezoid: A quadrilateral with only one pair of
parallel sides
2. Bases: The parallel sides of a trapezoid
3. Legs of a Trapezoid:
4. Base Angles:
5. Isosceles Trapezoid:
6. Vocabulary
1.Trapezoid: A quadrilateral with only one pair of
parallel sides
2. Bases: The parallel sides of a trapezoid
3. Legs of a Trapezoid: The sides that are not parallel in a
trapezoid
4. Base Angles:
5. Isosceles Trapezoid:
7. Vocabulary
1.Trapezoid: A quadrilateral with only one pair of
parallel sides
2. Bases: The parallel sides of a trapezoid
3. Legs of a Trapezoid: The sides that are not parallel in a
trapezoid
4. Base Angles: The angles formed between a base and
one of the legs
5. Isosceles Trapezoid:
8. Vocabulary
1.Trapezoid: A quadrilateral with only one pair of
parallel sides
2. Bases: The parallel sides of a trapezoid
3. Legs of a Trapezoid: The sides that are not parallel in a
trapezoid
4. Base Angles: The angles formed between a base and
one of the legs
5. Isosceles Trapezoid: A trapezoid that has congruent
legs
10. Vocabulary
6. Midsegment of a Trapezoid: The segment that
connects the midpoints of the legs of a trapezoid
7. Kite:
11. Vocabulary
6. Midsegment of a Trapezoid: The segment that
connects the midpoints of the legs of a trapezoid
7. Kite: A quadrilateral with exactly two pairs of
consecutive congruent sides; Opposite sides are not
parallel or congruent
14. Theorems
Isosceles Trapezoid
6.21: If a trapezoid is isosceles, then each pair of base
angles is congruent
6.22: If a trapezoid has one pair of congruent base
angles, then it is isosceles
6.23:
15. Theorems
Isosceles Trapezoid
6.21: If a trapezoid is isosceles, then each pair of base
angles is congruent
6.22: If a trapezoid has one pair of congruent base
angles, then it is isosceles
6.23: A trapezoid is isosceles IFF its diagonals are
congruent
17. Theorems
6.24 - Trapezoid Midsegment Theorem: The midsegment
of a trapezoid is parallel to each base and its measure
is half of the sum of the lengths of the two bases
Kites
6.25:
6.26:
18. Theorems
6.24 - Trapezoid Midsegment Theorem: The midsegment
of a trapezoid is parallel to each base and its measure
is half of the sum of the lengths of the two bases
Kites
6.25: If a quadrilateral is a kite, then its diagonals are
perpendicular
6.26:
19. Theorems
6.24 - Trapezoid Midsegment Theorem: The midsegment
of a trapezoid is parallel to each base and its measure
is half of the sum of the lengths of the two bases
Kites
6.25: If a quadrilateral is a kite, then its diagonals are
perpendicular
6.26: If a quadrilateral is a kite, then exactly one pair of
opposite angles is congruent
20. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
21. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
22. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
360 − 2(130)
23. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
360 − 2(130) = 100
24. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
360 − 2(130) = 100
100/2
25. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
360 − 2(130) = 100
100/2 = 50
26. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
360 − 2(130) = 100
100/2 = 50
m∠MJK = 50°
27. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
360 − 2(130) = 100
100/2 = 50
m∠MJK = 50°
or
28. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
360 − 2(130) = 100
100/2 = 50
m∠MJK = 50°
or
ML ! JK
29. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
360 − 2(130) = 100
100/2 = 50
m∠MJK = 50°
or
ML ! JK
m∠MJK + m∠JML =180
30. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
360 − 2(130) = 100
100/2 = 50
m∠MJK = 50°
or
ML ! JK
m∠MJK + m∠JML =180
m∠MJK +130 =180
31. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
a. m∠MJK
m∠JML = m∠KLM
360 − 2(130) = 100
100/2 = 50
m∠MJK = 50°
or
ML ! JK
m∠MJK + m∠JML =180
m∠MJK +130 =180
m∠MJK = 50°
32. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
b. JL
33. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
b. JL
JN = KN
34. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
b. JL
JN = KN
JL = JN + LN
35. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
b. JL
JN = KN
JL = JN + LN
JL = 6.7 + 3.6
36. Example 1
Each side of a basket is an isosceles trapezoid. If m∠JML =
130°, KN = 6.7 ft, and LN = 3.6 ft, find each measure.
b. JL
JN = KN
JL = JN + LN
JL = 6.7 + 3.6
JL = 10.3 ft
37. Example 2
Quadrilateral ABCD has vertices A(5, 1), B(−3, −1), C(−2, 3),
and D(2, 4). Show that ABCD is a trapezoid and determine
whether it is an isosceles trapezoid.
38. Example 2
Quadrilateral ABCD has vertices A(5, 1), B(−3, −1), C(−2, 3),
and D(2, 4). Show that ABCD is a trapezoid and determine
whether it is an isosceles trapezoid.
x
y
39. Example 2
Quadrilateral ABCD has vertices A(5, 1), B(−3, −1), C(−2, 3),
and D(2, 4). Show that ABCD is a trapezoid and determine
whether it is an isosceles trapezoid.
x
y
A
40. Example 2
Quadrilateral ABCD has vertices A(5, 1), B(−3, −1), C(−2, 3),
and D(2, 4). Show that ABCD is a trapezoid and determine
whether it is an isosceles trapezoid.
x
y
A
B
41. Example 2
Quadrilateral ABCD has vertices A(5, 1), B(−3, −1), C(−2, 3),
and D(2, 4). Show that ABCD is a trapezoid and determine
whether it is an isosceles trapezoid.
x
y
A
B
C
42. Example 2
Quadrilateral ABCD has vertices A(5, 1), B(−3, −1), C(−2, 3),
and D(2, 4). Show that ABCD is a trapezoid and determine
whether it is an isosceles trapezoid.
x
y
A
B
C
D
43. Example 2
Quadrilateral ABCD has vertices A(5, 1), B(−3, −1), C(−2, 3),
and D(2, 4). Show that ABCD is a trapezoid and determine
whether it is an isosceles trapezoid.
x
y
A
B
C
D
44. Example 2
Quadrilateral ABCD has vertices A(5, 1), B(−3, −1), C(−2, 3),
and D(2, 4). Show that ABCD is a trapezoid and determine
whether it is an isosceles trapezoid.
x
y
A
B
C
D
We need AB to be parallel
with CD
45. Example 2
Quadrilateral ABCD has vertices A(5, 1), B(−3, −1), C(−2, 3),
and D(2, 4). Show that ABCD is a trapezoid and determine
whether it is an isosceles trapezoid.
x
y
A
B
C
D
We need AB to be parallel
with CD
CB ≅ ADAlso,