Download Comparing Types of Proofs

Sect. 3.2 Proof and Perpendicular
Lines.
Goal 1
Comparing Types of Proofs
Goal 2
Proving Results about
Perpendicular Lines
Comparing Types of Proofs
F
a) Name a line that appears to
be parallel to
EH
be parallel to
D
C
HC
c) Name a line that appears to
be skew to
H
G
b) Name a line that appears to
E
A
B
BC
d) Name a plane that appears to be parallel to plane GDA.
Comparing Types of Proofs
Theorem 3.1
If two lines intersect to form a
linear pair of congruent angles,
then the lines are perpendicular.
g
gh
h
Comparing Types of Proofs
Theorem 3.2
If two sides of two adjacent
acute angles are perpendicular,
then the angles are
complementary.
2
1
1 and 2 are
complementary.
Comparing Types of Proofs
Theorem 3.3
If two lines are perpendicular,
then they intersect to form four
right angles.
Proving Results About Perpendicular Lines
A
Example 2
Given: AB  BC
Prove: 1 and 2 are complementary
Statements
2
1
B
Reasons
1. AB  BC
1. Given
2. ABC is a right angle
2. def. of perpendicular lines
3. m ABC = 90°
3. def. of right angle
4. m1 + m2 = m ABC
4. Angle Addition Postulate
5. m1 + m2 = 90°
5. Substitution
6. 1 and 2 are complements
6. def. of complementary angles
C
Given: 1 is a right angle
Prove: 3 is a right angle
1
3
Given: 1 is a right angle
Prove: 3 is a right angle
1
3
1  3
a.
1 is a right 
b.
m1 = m3
m1 = 90°
d.
c.
m 3 = 90°
e.
3 is a right 
f.
Homework
3.2 11-16, 18, 26, 27, 29-36