Why are mathematical proofs important?

Of four points are collinear, they are also coplanar

Are the corresponding angles congruent? explain why or why not.

Look at the figure below: triangle abc is a right triangle with angle abc equal to 90 degrees. the length of ac is 5 units and the length of ab is 4 units. d is a point above c. triangle adc is a right triangle with angle dac equal to 90 degrees and dc parallel to ab. what is the length, in units, of segment cd?