1. Honors Geometry
Unit 4 Project 1, Parts 3 and 4

2. Part 3A
On a sheet of paper, construct a scalene triangle of sides 14cm, 12cm and 10cm.
Label the vertices A, B, and C.
Draw a line from C perpendicular to side AB
Draw a line from A perpendicular to side BC
Draw a line from B perpendicular to side AC.
Label the points H, I and J, respectively.
Label the Point of Concurrency K

3. Part 3A Analysis
Answer the question on the answer sheet.

4. Part 3B Repeat Part 3A for: An obtuse scalene triangle
A right scalene triangle
An isosceles triangle
An equilateral triangle
Answer the question on the answer sheet.

5. Altitudes of a triangle
A perpendicular segment from a vertex to the opposite side (or the extension of the other side) is called an altitude of the triangle.
An altitude can be thought of as the height of the triangle for a given base (the side it is perpendicular to).
The point of concurrency of the altitudes is called the orthocenter.

6. Part 4A
On a sheet of paper, construct a scalene triangle of sides 14cm, 12cm and 10cm.
Label the vertices A, B, and C.
Draw the angle bisector of angle A.
Draw the angle bisector of angle B.
Draw the angle bisector of angle C.

7. Part 4B Label the Point of Concurrency L
Draw perpendicular segments from L to AB, BC and AC
Label the points on the sides M, N, O, respectively
Measure LM, LN and LO and record

8. Part 4C
Using your compass, draw a circle with a center at L that contains points M, N and O
Record your observations

9. Part 4D Repeat Parts 4A and 4B for: An obtuse scalene triangle
A right scalene triangle
An isosceles triangle
An equilateral triangle
Answer the question on your answer sheet.

10. Part 4E
In each of the triangles from part 4D, try drawing the same circle as you did in part 4C
Record your observations

11. Angle Bisectors and the inscribed circle
The point of concurrency of the angle bisectors in called the incenter.
The incenter is the center of the inscribed circle. (Inscribed means to be drawn within)

12. The Angle Bisector Theorem
Any point on the angle bisector of an angle is equidistant from the sides of the angle.