TEST

"Make sure you know all the information before taking a test. If you don't, then stay after school and ask the teacher for some one-on-one time so you can fully understand" -Allison DeBord

1. In ABC, point H is the centroid. BH=4x-6, HF=x

Find: x

SOLUTION

2. Given: ABC with midpoints F, D, and E on sides BC, AC, and AB, respectively. Where the midlines meet is point O. Perpendicular lines are drawn from the center (O) to the triangle's sides. These are labeled I, H, and G on sides BC, AC, and AB, respectively.

AB=3.3 cm, BC=6cm, AC=4.2 cm, OG=1.3 cm, OH=1.1 cm, and OI=0.7 cm.

PROVE: that point O is the centroid by finding the areas of triangles BOA, BOC, and AOC and tell why these areas prove that O is the centroid.

SOLUTION

3. This problem is called Napoleons Triangle. It's very difficult, but see if you can prove it using your knowledge of triangles and triangle centers. Good Luck!

THEOREM:

Given any triangle,ABC, construct equilateral triangles on the exterior sides of ABC. The segments connecting the centroids of the equilateral triangles form an equilateral triangle.

NEED A HINT?

SOLUTION

4. Given: ABC with midlines AE, BD, and CF. The midlines meet at centroid H. Point G is on side AB. HG is height of ABH. AB=10 cm. Area of BHC is 40 cm².

FIND: GH

SOLUTION

5. Given: O is the centroid ofABC. AH is height of AOC. AH=2. AC=7

FIND: Area of ABC

SOLUTION