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