HONORS GEOMETRY 4.2. Angles of Triangles. Do Now: Classify the following triangles and then find x and ?.

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Presentation transcript:

HONORS GEOMETRY 4.2. Angles of Triangles

Do Now: Classify the following triangles and then find x and ?.

Homework Questions? Comments? Confusions? ASK ASK ASK!

Exterior Angles Definition Formed by one side of the triangle and the extension of an adjacent side.

Remote Interior Angles Angles not adjacent to the exterior angle

Example One: The interior angles The exterior angle The remote interior angles of ∠ 4

Exterior Angle Theorem The measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Let’s Prove It!

Example Two:

Example Three:

You Try! Find the missing angles

Example Four:

You Try! Find x

Theorem: The acute angles of a right triangle are complementary <A and <B are complementary

How do we know?

2 nd Theorem: There can be at most one right or obtuse angle in a triangle If <C is right or obtuse, <A and <B are both acute

Why!?!?!

Practice Problems Try some on your own/in small groups We will be playing around with this some more on Monday.

Exit Ticket: Find m<2