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Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) B A C Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) B A C Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) B A C The parallel postulate allows us to draw a line through point B that is parallel to AC. Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) 3 A B 2 1 C Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) 3 A B 2 1 C Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) 3 A B 2 1 C Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) 3 A B 2 1 C Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. B A 1 C Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. B A 1 C Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. B A 1 C Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. B A 1 C Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. B A 1 C Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. B A 1 C Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B A C Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E • C Points D and E are midpoints. Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E • C Points D and E are midpoints. Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E • C Points D and E are midpoints. Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C Extend DE so that E is the midpoint of DF. Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C We can draw CF, because two points determine a line. Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C Triangle BED is congruent to triangle CEF by SAS. Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C ADFC is a parallelogram, because one pair of opposite sides is both parallel and congruent. Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A DF E F • C to AC, because opposite sides of a parallelogram are parallel. Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C DE to AC, because DE is part of DF. Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem) B D • A E F • C Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Theorem 50: The sum of the measures of the three angles of a triangle is 180º. (Triangle Sum Theorem) Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem)