1. In the figure, LMNO is a rhombus. Find x.

2. Find y.

3. In the figure, QRST is a square.

Find n if mTQR = 8n + 8.

4. Find w if QR = 5w + 4 and RS = 2(4w –7).

5. Find QU if QS = 16t – 14 and QU = 6t + 11.

• trapezoid

• isosceles trapezoid

• median

• Recognize and apply the properties of trapezoids.

• Solve problems involving the medians of trapezoids.

http://www.ca.geometryonline.com/

Proof of Theorem 6.19

Write a flow proof.

Given: KLMN is an isosceles trapezoid.

Prove:

Proof of Theorem 6.19

Proof:

Write a flow proof.

Given: ABCD is an isosceles trapezoid.

Prove:

A. A

B. B

C. C

D. D

A. Substitution

B. Definition of trapezoid

C. CPCTC

D. Diagonals of an isosceles trapezoid are .

Which reason best completes the flow proof?

Proof:

The top of this work station appears to be two adjacent trapezoids. Determine if they are isosceles trapezoids.

Each pair of base angles is congruent, so the legs are the same length.

Answer: Both trapezoids are isosceles.

Identify Isosceles Trapezoids

1. A.

2. B.

3. C.

The sides of a picture frame appear to be two adjacent trapezoids. Determine if they are isosceles trapezoids.

A. yes

B. no

C. cannot be determined

Identify Trapezoids

A. ABCD is a quadrilateral with vertices A(5, 1), B(–3, –1), C(–2, 3), and D(2, 4). Verify that ABCD is a trapezoid.

A quadrilateral is a trapezoid if exactly one pair of opposite sides are parallel. Use the Slope Formula.

Identify Trapezoids

slope of

slope of

slope of

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

Identify Trapezoids

B. ABCD is a quadrilateral with vertices A(5, 1), B(–3, 1), C(–2, 3), and D(2, 4). Determine whether ABCD is an isosceles trapezoid. Explain.

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.

http://www.ca.geometryonline.com/

Median of a Trapezoid

A. DEFG is an isosceles trapezoid with medianFind DG if EF = 20 and MN = 30.

Answer: DG = 40

Median of a Trapezoid

Theorem 8.20

Multiply each side by 2.

Substitution

Subtract 20 from each side.

Median of a Trapezoid

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

Because this is an isosceles trapezoid,

Median of a Trapezoid

Consecutive Interior Angles Theorem

Substitution

Combine like terms.

Divide each side by 9.

Answer: 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. XY = 32

B. XY = 25

C. XY = 21.5

D. XY = 11

A. WXYZ is an isosceles trapezoid with medianFind XY if JK = 18 and WZ = 25.

A. A

B. B

C. C

D. D

A. m3 = 60

B. m3 = 34

C. m3 = 43

D. m3 = 137

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