1. The distance from a point to a line is the length of the perpendicular segment from the point to the line.
Think of it as height (altitude) since it always
has to form a right angle.

2. perpendicular T
right angles
linear pair of
congruent angles a T b

3. complementary
congruent linear pairs form perpendicular lines.
Given
PS PQ T
Theorem 3.10
Angles with a sum
of 90 are complementary

4. Since c d, angles 1, 2, 3 and 4 form right angles.
That means ∠3 + ∠4 = 180 T
congruent linear pairs form perpendicular lines.
Given
Theorem 3.8
Theorem 3.9
perpendicular lines
form right angles.

5. perpendicular T
parallel ll

6. x
t ll s
x ll y
x z
x ll z
x y ll z
Yes, because c and d are both perpendicular to a, c ll d by Theorem 3.12.
Yes, because b c, and c ll, d as explained in
exercise 3, then b d by Theorem 3.11. T

7. 34 71 21 20 34 71 40
-42 - 20 21
58 inches

8. m =
y2 - y1
x2 - x1
m1 =
3 - 0
-2 - (-3)
= 3
m2 =
5 - 2
2 - 1
m3 =
3 - 2
-2 - 1
= -1/3
d = √(x2 - x1)2 + (y2 - y1)2
d = √(x2 - x1)2 + (y2 - y1)2
= √(1-(-2))2 + (2 - 3)2
≈ 3.162un