Segment and Angle Proofs

If two quantities are equal, subtracting the same amount from both sides maintains the equality. For example, if $$a = b$$ , then $$a - c = b - c$$ .

If $$a = b$$ and $$b = c$$ , then $$a = c$$ . This property allows us to conclude equality through a chain of equalities.

Two angles are supplementary if the sum of their measures is $$180^\text{o}$$ .

Vertical angles are opposite angles formed by two intersecting lines, and they are always congruent.

If point D is in the interior of angle ABC, then $$\text{m}\text{∠}ABC = \text{m}\text{∠}ABD + \text{m}\text{∠}DBC$$ .

A linear pair consists of two adjacent angles whose non-common sides form a straight line. They are supplementary.

An angle bisector is a ray that divides an angle into two equal parts.

If angle A is congruent to angle B, then angle B is congruent to angle A.

If two quantities are equal, adding the same amount to both sides maintains the equality. For example, if $$a = b$$ , then $$a + c = b + c$$ .

Two angles are congruent if they have the same measure.