Question

in exercises 7 and 8, find the length of the midsegment of the trapezoid. (see example
7.
8.
in exercises 9 and 10, find ab.
9.
10.
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Explanation:

Step1: Recall trapezoid midsegment formula

The midsegment length of a trapezoid is $\frac{\text{sum of the two bases}}{2}$.
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For Exercise 7:

Step1: Identify bases and midsegment

Bases: $18, 10$; Midsegment = $MN$

Step2: Calculate midsegment length

$\frac{18 + 10}{2} = \frac{28}{2} = 14$
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For Exercise 8:

Step1: Identify bases and midsegment

Bases: $76, 57$; Midsegment = $MN$

Step2: Calculate midsegment length

$\frac{76 + 57}{2} = \frac{133}{2} = 66.5$
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For Exercise 9:

Step1: Set up midsegment equation

Let $AB = x$, midsegment $=7$, base $DC=10$.
$\frac{10 + x}{2} = 7$

Step2: Solve for $x$

Multiply both sides by 2: $10 + x = 14$
Subtract 10: $x = 14 - 10 = 4$
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For Exercise 10:

Step1: Set up midsegment equation

Let $AB = x$, midsegment $=18.7$, base $DC=11.5$.
$\frac{11.5 + x}{2} = 18.7$

Step2: Solve for $x$

Multiply both sides by 2: $11.5 + x = 37.4$
Subtract 11.5: $x = 37.4 - 11.5 = 25.9$

Answer:

1. $14$
2. $66.5$
3. $AB = 4$
4. $AB = 25.9$