SECTION 2-5: PERPENDICULAR LINES

Definition of Perpendicular lines: are two lines that intersect to form right angles (90° angles). Ex:

1. If , then m1 = 90°.

2. If m1 = 90°, then .

3. If , then 1 is a right angle.

4. If 1 is a right angle, then .

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THEOREM 2-4 If two lines are perpendicular, then they form congruent adjacent angles.

If , then m1 = m4.

THEOREM 2-5 If two lines form congruent adjacent angles, then the lines are perpendicular.

If m1 = m4, then .

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THEOREM 2-6 If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

If , then AOB and BOC are complementary angles.

If two angles are supplements of congruent angles (or the same angle), then the two angles are congruent.

If 1 and 2 are supplementary and 3 and 4 are supplementary and 1 3, then 2 4.

1 2

3 4

If two angles are complements of congruent angles (or the same angle), then the two angles are congruent.

If is complementary to 5 and 6 is complementary to 5, then 4 6.

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Examples: ⊥ . Use the diagram to classify each statement as true or false.

1. ⊥

2. CGB is a right angle.

3. CGA is a right angle.

4. mDGB = 90

5. EGC and EGA are complements.  6. DGF is complementary to DGA.

7. EGA is complementary DGF.

False

False

True

True

True

True

True

Complete with always, sometimes, or never.

8. Perpendicular lines _________ lie in the same plane.  9. Two lines are perpendicular if and only if they ______________ form congruent adjacent angles.  10. Perpendicular lines ____________ form 60° angles.

always

always

never

Complete with always, sometimes, or never.

11. If the exterior sides of two adjacent angles are perpendicular, then the angles are _____________ supplementary. 12. If a pair of vertical angles are supplementary, the lines forming the angles are ______________ perpendicular.

always

never

Homework:

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