9-3: The Parallel Postulate 9-4: Triangles: Quick Revisit Proof Geometry
Alternate Interior Parallel Converse What did Alternate Interior Parallel Theorem say, again? If alternate interior angles are congruent then lines are parallel. Therefore its converse says…
Alternate Interior Parallel Converse If two parallel lines are cut by a transversal, then alternate interior angles are congruent. then
Alt. Int. Parallel Converse Proof If two parallel lines are cut by a transversal, then alternate interior angles are congruent. Given: Parallel lines L1 and L2 with transversal T intersecting them at P and Q Suppose: a and b are not congruent(supposition) Then: Let L be the line through P for which alternate interior angles are congruent. Then L || L2. But: It is given that L1||L2. The Parallel Postulate assures only one parallel line through external point. (the CONTRADICTION) So: a b
The Corresponding Angles Parallel Converse What did Corresponding Angles Parallel say, again? If corresponding angles are congruent then lines are parallel. Therefore its converse says…
The Corresponding Angles Parallel Converse If two parallel lines are cut by a transversal, then corresponding angles are congruent. then
Same Side Angle Parallel Converse What did Same Side Angle Parallel say, again? If same side interior angles are supplementary then lines are parallel. Therefore…
Same Side Angle Parallel Converse If two parallel lines are cut by a transversal, then same side interior angles are supplementary. then m2 + m3 = 180 and m1 + m4 = 180
Revisit Triangle Sum Theorems The sum of the interior angles in a triangle is 180˚.
Triangle Fundamentals Proof of triangle sum theorem
Third Angles Theorem Third Angles Theorem:
Homework pg. 275-276: #5 – 11 odd, 16 pg. 279-280: #2, 5, 7, 8