Question

complete all problems on pg 24 - 25 of the unit 4 packet and then complete this assignment.
1 numeric 2 points
1.
provide the value of the missing segment. give only the number.
answer

Explanation:

Step1: Use the triangle mid - segment theorem

The triangle mid - segment theorem states that a mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is parallel to the third side and half its length. In the given figure, the segment of length \(15\) is a mid - segment. Let the length of the missing segment be \(x\).
The ratio of the sides of the similar triangles (formed by the mid - segment) gives the proportion. If we consider the sides of the two triangles (the smaller one with side \(15\) and the larger one with the missing side \(x\) and the sides \(6\) and \(8\) in the smaller and larger triangles respectively).
Since the segment with length \(15\) is a mid - segment (because of the mid - point markings), we can also use the property of similar triangles. The two triangles are similar by the Side - Side - Side (SSS) similarity criterion (the ratio of the sides of the smaller triangle to the larger triangle is constant). The ratio of the sides of the smaller triangle to the larger triangle for the non - mid - segment sides is \(\frac{6}{8}=\frac{3}{4}\), but using the mid - segment property directly:
The mid - segment of a triangle is parallel to the third side and half its length. Wait, no, actually, if we consider the two triangles (the smaller one with side \(15\) and the side \(6\) and the larger one with the missing side \(x\) and side \(8\)).
We know that \(\frac{15}{x}=\frac{6}{8}\) (by the similarity of triangles, corresponding sides are in proportion). Cross - multiply: \(6x = 15\times8\).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(20\)