Section 3.2
Theorems About Perpendicular Lines
Theorem 3.1: All right angles are congruent.
If$∠A = 90* andm∠B = 90* ,
then∠A ≅ ∠B.
Theorem 3.2: If 2 lines are perpendicular, then they intersect to form 4 right angles.
If6 ⊥ $, then$∠1 = 90* ,
$∠2 = 90* ,
$∠3 = 90* ,
and $∠4 = 90* .
Theorem 3.3: If 2 lines intersect to form adjacent congruent angles, then the lines are
perpendicular.
>????@ ⊥ AB
>????@ .
If$∠1 ≅ ∠2, then<=
Theorem 3.4: If 2 sides of adjacent angles are perpendicular, then the angles are complementary.
?????@ ⊥ CE
??????@ , then$∠3 + $∠4 = 90* .
IfCD
Examples
Determine whether enough information is given to conclude that the statement is true. Explain.
1.
∠6 ≅ ∠10
2.
∠7 ≅ ∠10
3.
∠6 ≅ ∠8
4.
∠7 ≅ ∠11
5.
∠7 ≅ ∠9
6.
∠6 ≅ ∠11
What can you conclude about ∠1 and ∠2 using the given information?
7.
BA ⊥ BC
8.
n⊥m
9.
Given a ⊥ b, find the value of x.
10.
11.
12.
13.
14.
15.
Given AB ⊥ BD , find the value of x and use it to find m∠CBD.
16.
17.
18.
h⊥k