Angle Relationships in Triangles

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Angle Relationships in Triangles

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Presentation transcript:

Angle Relationships in Triangles Paper! Pencil! Calculator!

Angle Sum Theorem

Auxiliary Line An auxiliary line is a line that is added to a figure to aid in a proof.

Example After an accident, the positions of cars are measured by law enforcement to investigate the collision. Use the diagram drawn from the information collected to find mXYZ.

Corollarys

Examples One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle? The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle?

Interior vs. Exterior An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side. 4 is an exterior angle. 3 is an interior angle.

Exterior Angle Theorem

Example Find mB.

Third Angles Theorem

Example Find m<P and m<T.

Assignment Pg. 228 #16-24 even, 42