Instruction: Construct a mid-segment of the given acute triangle.

Goal: 2L 5E 3V

Available Tools:

• Move
• Point
• Line
• Circle
• Perpendicular Bisector
• Perpendicular
• Angle Bisector
• Parallel
• Non-collapsing Compass
• Intersect

Pack: Iota

Previous Level: 9.9

Next Level: 10.1

## 2L Solution

Let A, B, and C be the vertices of the triangle.

1. Construct the perpendicular bisector of AB, intersecting AB at D.
2. Construct the line parallel to BC through D.

## 5E Solution

Let A, B, and C be the vertices of the triangle.

1. Construct a circle with an arbitrary center D on AB and radius AD, intersecting AB at E.
2. Construct circle E with radius AE, intersecting BC at F and G, if the circle doesn't intersect BC at two points move D so that it does.
3. Construct line AF, intersecting circle D at H.
4. Construct line AG, intersecting circle D at I.
5. Construct line HI.

## 3V Solution

From the 2L Solution

1. Let the intersection between the parallel line and AC be E.
2. Construct the line parallel to AC through D, intersecting BC at F.
3. Construct line EF.