# Parallel Lines and Proportional Parts Worksheet

Parallel Lines and Proportional Parts Worksheet
• Page 1
1.
If $x$ is the length of $\stackrel{‾}{\mathrm{MN}}$ which is the midsegment of ΔABC, then find the value of $\stackrel{‾}{\mathrm{BC}}$.

 a. 2$x$ units b. $x$ units c. 3$x$ units d. 4$x$ units

2.
In the given triangle if $\stackrel{‾}{\mathrm{FG}}$ is midsegment of ΔAED and $\stackrel{‾}{\mathrm{DE}}$ is the midsegment of ΔACB, then find the value of $x$.

 a. 20 units b. 25 units c. 30 units d. 15 units

3.
Given a regular hexagon with one of its base as 10 cm, it was cut into co-triangles with center $O$. What is the sum of the length of all the midsegments of all the triangles?

 a. 60 cm b. 30 cm c. 36 cm d. 24 cm

4.
Find the length of mid-segment $\stackrel{‾}{\mathrm{EF}}$.

 a. $\frac{\sqrt{104}}{2}$ units b. 52 units c. $\sqrt{105}$ units d. $\sqrt{104}$ units

 a. Distance from O to A = Distance from C to B = Distance from P to Q b. (Slope of $\stackrel{‾}{\mathrm{PQ}}$ × Slope of $\stackrel{‾}{\mathrm{OA}}$) = - 1, (Slope of $\stackrel{‾}{\mathrm{PQ}}$ × Slope of $\stackrel{‾}{\mathrm{CB}}$) = - 1 c. Slope of $\stackrel{‾}{\mathrm{PQ}}$ = Slope of $\stackrel{‾}{\mathrm{OA}}$ = Slope of $\stackrel{‾}{\mathrm{CB}}$ d. Midpoint of $\stackrel{‾}{\mathrm{PQ}}$ = Midpoint of $\stackrel{‾}{\mathrm{OA}}$ = Midpoint of $\stackrel{‾}{\mathrm{CB}}$