Page 35 - Math Course 3 (Book 2)

Properties of Trapezoids

Median of a Trapezoid
Your Turn!

Example Proof of Theorem 7.19

E F Write a flow proof.
3 4 Given: ABCD is an isosceles trapezoid.
M N
Prove: ∠CBD ≅ ∠BCA
D 1 2 G

DEFG is an isosceles trapezoid with median MN. ABCD is an isosceles trapezoid.
Find DG if EF = 20 and MN = 30. Given

1
MN = (EF + DG) Theorem 7.20 AB ≅ DC AC ≅ DB BC ≅ CB
2
Def. of isos. ??? Reflexive Prop.
1
30 = (20 + DG) Substitution trap. are.
2

60 = 20 + DG Multiply each side by 2 △ABC ≅ △DCB
SSS
40 = DG Subtract 20 from each side
∠CBD ≅ ∠BCA
SSS

Answer DG = 40 A. Substitution
B. Definition of trapezoid
C. CPCTC
D. Diagonals of an isosceles trapezoid are ≅.
E F
3 4 Answer
M N

D 1 2 G Median of a Trapezoid
Z
Find m∠1, m∠2, m∠3, and m∠4 if m∠1 = 3x + 5 and K
m∠3 = 6x – 5. Y 2
4
Since EF || DG, ∠1 and ∠3 are supplementary.
Because this is an isosceles trapezoid, ∠1 ≅ ∠2
and ∠3 ≅ ∠4. 3
X
Consecutive Interior J 1
m∠1 + m∠3 = 180
Angles Theorem. W
WXYZ is an isosceles trapezoid with median JK
3x + 5 + 6x – 5 = 180 Substitution. Find XY if JK = 18 and WZ = 25.

A. XY = 32 B. XY = 25
9x = 180 Combine like terms. C. XY = 21.5 D. XY = 11

Answer
x = 20 Divide each side by 9.
If m∠2 = 43, find m∠3.

If x = 20, then m∠1 = 65 and A. m∠3 = 60 B. m∠3 = 34
m∠3 = 115. Because ∠1 ≅ ∠2 C. m∠3 = 43 D. m∠3 = 137
Answer
and ∠3 ≅ ∠4, m∠2 = 65 and
m∠4 = 115. Answer

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