3.6 - PROVE THMS
ABOUT PERP. LINES
Some Theorems about Perpendicular Lines
Thm 3.8 - If two lines intersect to form a
linear pair of congruent angles, then the
lines are perpendicular.
Some Theorems about Perpendicular Lines
Thm 3.9 - If two lines are perpendicular, then
they intersect to form four right angles.
Thm 3.10 - If two sides of two adjacent acute
angles are perpendicular, then the angles are
complementary.
Example 1) In the diagram, AB ⊥ BC. What
can you conclude about ∠1 and ∠2?
A
D
1 2
B
C
Example 2) Prove Theorem 3.10 - If two sides
of two adjacent acute angles are
perpendicular, then the angles are
complementary.
Given: ED ⊥ EF
Prove: ∠7 and ∠8 are complements
8
F
D
7
E
Some Theorems about Perpendicular Lines
Thm 3.11 - Perpendicular Transversal - If a
transversal is perpendicular to one of two
parallel lines, then it is perpendicular to the
other.
Some Theorems about Perpendicular Lines
Thm 3.12 - Lines Perpendicular to
Transversal - In a plane, if two lines are
perpendicular to the same line, then they are
parallel to each other.
Exit Problem) Find the measure of ∠1.
65˚
1