Uses arrows to show the flow of the logical argument
Right Angle Congruence Theorem 1. Two Column Proof: All right angles are congruent. Given : 1 and 2 are right angles Prove : 1 ≅ 2 Statement Reason 1 and 2 are right angles Given m 1 = 90 o , m 2 = 90 o Definition of a right angle m 1 = m 2 Transitive property of equality 1 ≅ 2 Definition of congruent angles
Because angles 1 and 2 are right angles, their measures are equal to 90 o , by the definition of right angles. Hence by the transitive property of equality, the measure of angle 1 is equal to the measure of angle 2. By the definition of congruent angles, angle 1 is congruent to angle 2.
If two lines are perpendicular, then they intersect to form four right angles.
Proof of Theorem 3.2 Prove : 1 + 2 are complementary Statement Reason AB BC Given ABC is a right angle Definition of perpendicular lines m ABC = 90 o Definition of a right angle m 1 + m 2 = m ABC Angle addition postulate m 1 + m 2 = 90 o Substitution property of equality 1 + 2 are complementary Definition of complementary angles