4.3 Angle Relationships In Triangles
Triangle Sum Theorem --The sum of the angle measures of a triangle is 180 °.
m < A + m < B + m < C = 180 °
Auxiliary line—A line that is added to a diagram to aid in the proof. You must
state that in the proof.
Corollary-- a theorem whose proof follows directly from another theorem.
Corollary—The acute angles of a right triangle are complementary
Corollary—The measure of each angle of an equiangular triangle is 60 ° .
Interior—the set of all points inside the figure
Exterior—the set of all points outside the figure
Interior angle—formed by two sides of a polygon. In the figure below, <1, < 2, and
< 3 are interior angles.
Exterior angle—formed by one side of a polygon and extending the adjacent side.
In the figure below, < 4 is an exterior angle.
Remote interior angle—the angles that are not adjacent to the exterior angle.
Exterior Angle Theorem. –The measure of an exterior angle of a triangle is equal
to the sum of the measures of its remote (non-adjacent) interior angles.
m<4=m<1+m<2
Third Angles Theorem—If two angles of one triangle are congruent to two angles
of another triangle, then the third pair of angles are congruent.
If < Q
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< T and < R
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< U, then < P
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< S.
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