Question

evaluate independent practice
lesson 8.4 homework
complete problems 1 - 6 below for independent practice.
when you are finished, check the solutions with your teacher.

1. fill in the following statements.

\\(\overline{de} \parallel \underline{\quad}\\)
\\(2de = \underline{\quad}\\)

1. fill in the following statements.

\\(\overline{qp} \parallel \underline{\quad}\\)
\\(2rs = \underline{\quad}\\)

1. find the measurement of \\(ed\\).

1. find the measurement of \\(nl\\).

1. solve for \\(x\\).

1. solve for \\(x\\).

Explanation:

Identify midsegments in Questions 1 and 2

Using the Triangle Midsegment Theorem and Midsegment Properties knowledge points

• In Question 1, points \(D\) and \(E\) are midpoints of \(AB\) and \(AC\). Thus, segment \(DE\) is a midsegment.
• In Question 2, points \(R\) and \(S\) are midpoints of \(QT\) and \(PT\). Thus, segment \(RS\) is a midsegment.

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Calculate ED in Question 3

Using the Triangle Midsegment Theorem and Midsegment Properties knowledge points

• Points \(E\) and \(D\) are midpoints of \(HI\) and \(JI\).
• Therefore, \(ED\) is a midsegment parallel to \(HJ\).

$$ ED = \frac{1}{2} HJ = \frac{1}{2} (14) = 7 $$

Calculate NL in Question 4

Using the Triangle Midsegment Theorem and Midsegment Properties knowledge points

• Points \(U\) and \(V\) are midpoints of \(NM\) and \(LM\).
• Therefore, \(UV\) is a midsegment parallel to \(NL\).

$$ NL = 2 UV = 2 (8) = 16 $$

Solve for x in Question 5

Using the Triangle Midsegment Theorem and Solving Linear Equations knowledge points

• Points \(W\) and \(X\) are midpoints of \(AB\) and \(BC\).
• Thus, \(WX\) is a midsegment parallel to \(AC\).

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Solve for x in Question 6

Using the Triangle Midsegment Theorem and Solving Linear Equations knowledge points

• Points \(B\) and \(A\) are midpoints of \(UT\) and \(UV\).
• Thus, \(BA\) is a midsegment parallel to \(TV\).

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Answer:

No.	Answer
2	\(\overline{QP} \parallel \overline{RS}\)<br>\(2RS = QP\)
3	\(ED = 7\)
4	\(NL = 16\)
5	\(x = 12\)
6	\(x = -8\)