Proof and Perpendicular Lines Chapter 3 Section 3.2 Proof and Perpendicular Lines
Warm-Up
Three New Theorems Thm 3.1 If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular 1 2 1 2 lines are
Three New Theorems Thm 3.2 If two sides of adjacent acute angles are perpendicular, then the angles are complementary 1 2 Lines 1 and 2 are complementary
Three New Theorems Thm 3.3 If two lines are perpendicular, then they intersect to form 4 right angles Lines All 4 angles are right angles
State the reason for the conclusion Given: m1 = m 2 Conclusion: 1 2 Def. Angles 2. Given: 3 and 4 are a linear pair Conclusion: 3 and 4 are Supplementary Linear Pair Postulate
State the reason for the conclusion Given: 5 6 Conclusion: 6 5 Symmetric Prop 4. Given: x is the midpoint of Conclusion: Def. Midpoint
State the Reason for the Conclusion Given: bisects BAC Conclusion: BAD DAC Definition Angle Bisector
Find the value of x x + 38 = 90 x = 52 x –12 + 49 = 90 x + 37 = 90
Find the value of x x + 3x = 90 4x = 90 x =
Complete the Two-column Proof of Theorem 3.2 Statements Reasons 1. Given 2. Def. Lines 3. mDCE = 90 4. Segment Addition Post 5. 90 = m1 + m2 6. Def. Complementary Angles
Definition Vertical Angles Vertical Angle Theorem def. Angles Given Def. Right Angle Substitution