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Proofs
Lesson Objective
In the coming lesson, we'll explore geometric proofs related to triangles and parallel lines.
Previously Covered
In the section above, we reviewed basic three-dimensional figures and some of their properties.
A mathematical proof demonstrates that, based on one or more given facts, a statement must be true.
The proof itself is a sequence of statements, each justified by a postulate or a theorem, such as the
Isosceles Triangle Theorem which you will see in this lesson.
On the pages that follow are sample proofs that are meant to simultaneously familiarize you with proofs
and reinforce some of the concepts. Remember, the notation for similar is ~ and the symbol for
congruence is .
Theorems and Postulates You’ll Need
Parallel Axiom: If two lines, l and m, intersect a transversal so that the sum of the interior angles on the
same side of the transversal is equal to 180°, then l and m are parallel.
If two lines, l and m, intersect a transversal so that the sum of the interior angles on the same side of the
transversal is less than 180°, then l and m intersect on that side of the transversal.
