3.4 Angles of a Triangle

Friday in class we learned about corollaries and how to apply parallel line info to triangles.
This section also talked about the different types of triangles, but everyone should know them already. Scalene, right, isosceles, acute, etc.....

Vertex: The points where the segments meet.
Points o,1 &2 are vertices


Auxiliary Line: A line that you can add to a figure to help in a proof.

Line l is an auxiliary line

Corollary: -Like a theorem
- Used in proofs
- Proved using a theorem
- Can be rewritten without an if.....then statement

Theorem:
The sum of the measures of the angles of a triangle is 180.

These are the 4 corollaries that go with this theorem.

Corollary:

• If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.

• Each angle of an equiangular triangle has measure 60.
• In a triangle, there can be at most one right angle or obtuse angle.
• The acute angles of a right triangle are complementary.

Exterior Angle: Angles that are formed by extending a side of a figure. It is always supplementary to the adjacent interior angle.


Angles 1,2,& 3 are exterior angles


Remote Interior Angle: The exterior angle is equal to the sum of the remote interior angles. They are the angles farthest from the exterior angle.

Angles 3 and 2 are remote interior angles to angle 4.

Theorem:
The measure of an exterior angle of a triangle equals the sum of the measure of the two remote interior angles.


The next scribe is.......
Hollee