Theorem: If two lines intersect to form a linear pair
of congruent angles, then the lines are ___________________.
If 1 
2 , then __________________.
h
1
2
g
“Congruent angles of a linear pair are formed by perpendicular lines.”
Theorem: If two lines are perpendicular, then they
intersect to form four ___________________.
If a  b, then  1,  2,  3, and  4 are _____________________.
“Perpendicular lines intersect to form 4 right angles.”
Example 1: Draw Conclusions
⃡ . What can you
In the diagram at the right, ⃡𝐴𝐵 ⊥ 𝐵𝐶
conclude about  1 and  2.
Theorem: If two sides of two adjacent acute angles are
perpendicular, then the angles are ______________________.
⃡ ⊥ 𝐵𝐶
⃡ , then  1 and  2 are complementary.
If 𝐵𝐴
“Two adjacent angles formed by perpendicular lines are complementary.”
b
2
1
3 4
a
Example 2: Prove IT!
Prove that if two sides of two adjacent acute angles are perpendicular,
then the angles are complementary.
Given: 𝐸𝐷 ⊥ 𝐸𝐹
Prove: ∠7 and ∠8 are complementary
STATEMENTS
1. 𝐸𝐷 ⊥ 𝐸𝐹
REASONS
1.
2. 𝑚∠𝐷𝐸𝐹 is a right angle
2.  lines intersect to form 4 right ∠𝑠.
3. 𝑚∠𝐷𝐸𝐹 = 90°
3.
4. 𝑚∠7 + 𝑚∠8 = 𝑚∠𝐷𝐸𝐹
4.
5. 𝑚∠7 + 𝑚∠8 = 90°
5.
6.
6.
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines,
then it is ________________________________ to the other.
If ℎ ∥ 𝑘 and 𝑗 ⊥ ℎ, then ___________________.
Lines Perpendicular to a Transversal Theorem
In a plane, if two lines are perpendicular to the same line,
then they are ___________________________ to each other.
If 𝑚 ⊥ 𝑝 and 𝑛 ⊥ 𝑝, then __________________.
Example 3: Draw Conclusions
Determine which lines, if any, must be parallel in the diagram.
Explain your reasoning.
Proofs
Prove Perpendicular Transversal Thm.
Prove Lines Perpendicular to a
Transversal Theorem
Given: m  p, n  p
Prove: m n
Given: h k, j  h
Prove: j  k
1
j
1
2
2
Statements
1. m  p, n  p
Reasons
1. Given
2. 1 is a right angle 2.
 2 is a right angle
3. 1  2
3.
4. m n
4.
Statements
Reasons
1. h k, j  h
1. Given
2. 1  2
2.
3. m 1 = m 2
3.
4. 1 is a right angle 4.
5. m 1 = 90
5.
6. m 2 = 90
6.
7. 2 is a right angle 7.
8. j  k
8.