Notecards Unit 4 Triangle Properties.

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Presentation transcript:

Notecards Unit 4 Triangle Properties

Classify Triangles by Sides Definitions Classify Triangles by Sides

Classify Triangles by Angles Definitions Classify Triangles by Angles

Definitions Interior and Exterior Angles When the sides of a polygon are extended, other angles are formed. The original angles are the interior angles. The angles that form linear pairs with the interior angles are the exterior angles.

Triangle Sum Theorem Theorem The sum of the measures of the interior angles of a triangle is 180°. A B C

Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. A B C D

Corollary to Triangle Sum Theorem The acute angles of a right triangle are complementary. A B C

Side Angle Relationships in a Triangle

Definition of Midsegment A midsegment is a segment that connects the midpoints of two sides of a triangle. Every triangle has three midsegments. Line segment BD is a midsegment of triangle AEC

Midsegment Theorem Theorem The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. BD = ½ AE BD is parallel to AE

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A AB + BC > AC BC + AC > AB B C AC + AB > BC