Download Perpendicular lines are two lines that intersect to form right angles

GEOMETRY/TRIGONOMETRY 2
Name _______________________
Perpendicular lines () Definition:
 If two lines are perpendicular, then they form _______________.

If two lines form ____________________, then the lines are
perpendicular.
M
2 1
3 4
J
Theorem 2-4
K
N
If two lines are perpendicular,
then they form _________________, ________________ angles.
Theorem 2-5 (converse of 2-4)
If two lines form _________________, ________________ angles,
then the lines are perpendicular.
Theorem 2-6
B
If the exterior sides of two adjacent acute angles are perpendicular,
then the angles are ______________________.
D
If AB  AC,
then BAD and DAC are _______________________.
A
C
Name the definition or state the theorem that justifies the statement about the
diagram.
_______________________ 1) If AB  BC, then ABC is a right angle.
_______________________ 2) If BD  AC, then 3  4.
_______________________ 3) If DC  DA, then 7 and 8 are comp.
B
12
_______________________ 4) 4  5.
A
_______________________ 5) If 4  6, then AC  BD.
_______________________ 6) If 7 and 8 are comp., then m7 + m8 = 90.
_______________________ 7) If ADC is a right angle, then mADC = 90.
3 4
5 6
7 8
D
C
E
D
F
Given: BE  AC, BD  BF. Find the value of x.
2 3
1
A
4
B
C
8) m2 = 2x + 10, m3 = 40.
8) x = _______
9) m3 = 2x + 5, m4 = 3x.
9) x = _______
10) m1 = 2x, m2 = 2x + 10,
m3 = 3x - 20, m4 = 3x - 10.
10) x = _______
11) m1 = 3x + 1, m2 = 4x + 5, m3 = 2x + 13
11) x = _______
Complete the following proofs by supplying the missing statements and reasons.
A
12) Given: BA  AC;
2 1
1 is complementary to 3
Prove:
m2 = m3
3
C
Statements
D
B
Reasons
1) BA  AC
1) _________________________
2) 1 and 2 are complementary
2) _________________________
3) _________________________
3) Given
4) m1 + m2 = 90;
m1 + m3 = 90
4) _________________________
5) _________________________
5) _________________________
6) _________________________
6) Reflexive Property
7) _________________________
7) _________________________