3.2 theorems about perpendicular linesPresentation Transcript
Theorems About Perpendicular Lines
Comparing Types of Proofs
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.
2. Paragraph Proof
3. Flow Proof
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
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