Questions: Tennessee Geometry Sem2 Quiz 1.3.1- Midsegments of Triangles Solve for x . a. 10 b. 12 c. 3 d. 8

Solution Steps

In the given triangle \( \triangle KRL \), \( MS \) is a midsegment. By definition, a midsegment in a triangle is parallel to one side of the triangle and half its length.

Since \( MS \) is a midsegment, it is parallel to \( KR \) and half its length. Therefore, we can set up the equation: \[ MS = \frac{1}{2} KR \]

Given: \[ KR = 2x \] \[ MS = -10 + 2x \]

Substitute the given values into the equation: \[ -10 + 2x = \frac{1}{2} (2x) \]

Simplify the equation: \[ -10 + 2x = x \]

Subtract \( x \) from both sides: \[ -10 + x = 0 \]

Add 10 to both sides: \[ x = 10 \]

Final Answer