Trapezoids Chapter 6.6. TrapezoidDef: A Quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases. The non-parallel.

TrapezoidsTrapezoidsChapter 6.6Chapter 6.6

TrapezoidTrapezoidDef: Def:

A Quadrilateral with exactly one pair of parallel sides.A Quadrilateral with exactly one pair of parallel sides. The parallel sides are called the The parallel sides are called the basesbases.. The non-parallel sides are called the The non-parallel sides are called the legslegs.. A trapezoid has two pairs of base angles.A trapezoid has two pairs of base angles.

If the legs are congruent, then it is called an If the legs are congruent, then it is called an isosceles trapezoid.isosceles trapezoid.

TrapezoidTrapezoid Base

Base

Base Angles

Base Angles

Leg

Leg

Isosceles Trapezoid

Isosceles Trapezoid TheoremIsosceles Trapezoid Theorem

Isosceles Trapezoid Isosceles Trapezoid Each pair of base angles are Each pair of base angles are ..

Another Isosceles Trapezoid TheorAnother Isosceles Trapezoid Theoremem

Isosceles Trapezoid Isosceles Trapezoid Its diagonals are Its diagonals are ..

Midsegment Theorem for TrapezoidsMidsegment Theorem for TrapezoidsThe Median or Midsegment of a trapezoid is // The Median or Midsegment of a trapezoid is //

to each base and is one half the sum of the to each base and is one half the sum of the lengths of the bases. (average of the bases)lengths of the bases. (average of the bases)

Midsegment =Midsegment =

B1

B2

Midsegment

2

)( 21 bb )( 21 bb 2

1or

DEFGDEFG is an isosceles trapezoid with is an isosceles trapezoid with median (midsegment) MNmedian (midsegment) MN

Find Find mm1, 1, mm2, 2, mm3, and 3, and mm4 4 if if mm1 = 31 = 3xx + 5 and + 5 and mm3 = 63 = 6xx – 5. – 5.

WXYZWXYZ is an isosceles trapezoid with is an isosceles trapezoid with median (midsegment)median (midsegment)

Find Find XYXY if if JKJK = 18 and = 18 and WZWZ = 25. = 25.

ABCDABCD is a quadrilateral with vertices is a quadrilateral with vertices AA(5, 1), (5, 1), BB(–3, 1), (–3, 1), CC(–2, 3), and (–2, 3), and DD(2, 4). Determine (2, 4). Determine whether whether ABCDABCD is an isosceles trapezoid. is an isosceles trapezoid.

Explain.Explain.

Identify Trapezoids

slope of

slope of

slope of

Answer: Exactly one pair of opposite sides are parallel, So, ABCD is a trapezoid.

Identify Trapezoids

Answer: Since the legs are not congruent, ABCD is not an isosceles trapezoid.

Use the Distance Formula to show that the legs are congruent.

1. A

2. B

3. C

0%0%0%

A B C

A. QRST is a quadrilateral with vertices Q(–3, –2), R(–2, 2), S(1, 4), and T(6, 4). Verify that QRST is a trapezoid.

A. yes

B. no

C. cannot be determined

1. A

2. B

3. C

0%0%0%

A B C

B. QRST is a quadrilateral with vertices Q(–3, –2), R(–2, 2), S(1, 4), and T(6, 4). Determine whether QRST is an isosceles trapezoid.A. yes

B. no

C. cannot be determined

Median of a Trapezoid

A. DEFG is an isosceles trapezoid with median (midsegment)Find DG if EF = 20 and MN = 30.

B. DEFG is an isosceles trapezoid. Find m1, m2, m3, and m4 if m1 = 3x + 5 and m3 = 6x – 5.

Consecutive Int. Angles Thm.

Substitution

Combine like terms.

Divide each side by 9Answer: If x = 20, then m1 = 65 and m3 = 115.

Because 1 2 and 3 4, m2 = 65and m4 = 115.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. XY = 32

B. XY = 25

C. XY = 21.5

D. XY = 11

A. WXYZ is an isosceles trapezoid with median (midsegment)Find XY if JK = 18 and WZ = 25.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. m3 = 60

B. m3 = 34

C. m3 = 43

D. m3 = 137

B. WXYZ is an isosceles trapezoid.If m2 = 43, find m3.

HomeworkHomework

Chapter 6.6Chapter 6.6Pg 359Pg 359

3,4, 17-223,4, 17-22