Download Geometry Lesson 5.3 – Angle Bisectors

Name: ____________________
Date: _______________
Geometry
Period: __________
Lesson 5.3 – Angle Bisectors
Part I
1. On your patty paper, construct a large angle – it should take up a lot of the piece of paper.
2. Fold to construct the angle bisector, and unfold and draw a line in the crease.
3. Place two points on this ray, and label them.
4. Measure the distance from your points to the sides of the angle. Remember, to measure the
distance from a point to a line, we must measure the perpendicular distance.
5. What do you notice about the points on the angle bisector?
Conclusions:
The Angle Bisector Theorem (Thrm 5.5)
If a point is on the bisector of an angle, then it is ____________ from the ________s of the angle.
Converse of the Angle Bisector Theorem (Thrm 5.5)
If a point is _____________ from the _________s of an angle, then it lies on the ___________
of the angle.
Part II
1. On your patty paper, construct a large acute scalene triangle.
2. Fold to construct the angle bisectors of the three angles of the triangle.
3. On a second sheet of patty paper, construct a large obtuse scalene triangle.
4. Fold to construct the angle bisectors of the three angles of the triangle.
5. What seems to be true about the angle bisectors of a triangle? Write a conjecture:
The __________
_____________s of a triangle intersect at a _________
_________________ called the
__________________.
_____
6. Choose one of your triangles. Using another piece of patty paper, compare the distance from the
incenter to each of the vertices of the triangle, and from the incenter to the sides of the
triangle. What do you notice?
Conclusion:
The Concurrency of Angle Bisectors of a Triangle (Thrm. 5.7)
The concurrency of the angle bisectors of a triangle is called the ____________, and it is
__________ from the __________s of that triangle.
Extension:
7. Based on your two triangles, can you think of an instance where the incenter will be outside of the
triangle? Why, or why not? Explain.
Practice:
Challenge:
Use the Angle Bisector Theorem to prove that the incenter is equidistant from all three sides. Write
an informal paragraph proof below.