Converse of the Base Angles Theorem- If two angles of a triangle are congruent, then the triangle is isosceles.
Exterior Angles Theorem- An exterior angle on a triangle is equal to the sum of the two interior angles that are not adjacent to it.
Third Angles Theorem- If two triangles have two pairs of congruent angles, then the third pair of angles are also congruent.
We proved each of the above theorems. We talked about the general process for proofs- Use your given information, think about what the goal is. What would the second to last box probably be, to allow you to reach your final conclusion? Will you use substitution, transitive property, CPCTC? Can you show two triangles are congruent? Can you combine boxes into some new box?
Once again, make sure reasons and the boxes they link are actually related!
The distance from a point to a line is shortest path from that point to the line. This path will always be perpendicular to the line. Any other path is longer. (This fact allows us to create inequalities from diagrams with different paths from a point to a line.)
We also got extra practice with the segment addition postulate, specifically with the issue of overlapping segments, and then also practiced classifying triangles using the Pythagorean Thm and Hinge Thm.