PROPERTIES OF PARALLEL LINES

1
PROPERTIES OF PARALLEL LINES

• GOAL 1 TO IDENTIFY ltS FORMED BY 2 LINES AND A
  TRANSVERSAL.
• GOAL 2 TO USE PROPERTIES OF PARALLEL LINES.

2
ANGLES FORMED BY A TRANSVERSAL

• A TRANSVERSAL IS A LINE THAT INTERSECTS 2 OR MORE
  COPLANAR LINES AT DIFFERENT POINTS.
• THE ltS THAT ARE FORMED CAN BE CATAGORIZED INTO 4
  TYPES.

3
CORRESPONDING ANGLES

• 2 ANGLES THAT OCCUPY CORRESPONDING POSITIONS
• THERE ARE 4 PAIRS.
• EXAMPLE lt1 lt5

t
4
1
3
l
2
1
m
5
8
7
6
4
ALTERNATE INTERIOR ltS

• 2 ANGLES THAT LIE BETWEEN l m ON OPPOSITE SIDES
  OF t
• THERE ARE 2 PAIRS.
• EXAMPLE lt2 lt8

t
4
1
3
l
2
1
m
5
8
7
6
5
ALTERNATE EXTERIOR ltS

• 2 ltS THAT LIE OUTSIDE l AND m ON OPPOSITE SIDES
  OF t.
• THERE ARE 2 PAIRS
• EX lt1 AND lt7

t
4
1
3
l
2
1
m
5
8
7
6
6
CONSECUTIVE INTERIOR ltS

• 2 ltS THAT LIE BETWEEN l AND m ON THE SAME SIDE OF
  t.
• THERE ARE 2 PAIRS.
• EX lt2 AND lt5

t
4
1
3
l
2
1
m
5
8
7
6
7
CORRESPONDING ltS POSTULATE

• IF 2 PARALLEL LINES ARE CUT BY A TRANSVERSAL,
  THEN THE PAIRS OF CORRESPONDING ltS ARE CONGRUENT.

8
ALTERNATE INTERIOR ltS THEOREM

• IF 2 PARALLEL LINES ARE CUT BY A TRANSVERSAL,
  THEN THE PAIRS OF ALTERNATE INTERIOR ltS ARE
  CONGRUENT.

9
CONSECUTIVE INTERIOR ANGLES THEOREM

• IF 2 PARALLEL LINES ARE CUT BY A TRANSVERSAL,
  THEN THE PAIRS OF CONSECUTIVE INTERIOR ANGLES ARE
  SUPPLEMENTARY.

10
ALTERNATE EXTERIOR ANGLES THEOREM

• IF 2 PARALLEL LINES ARE CUT BY A TRANSVERSAL,
  THEN THE PAIRS OF ALTERNATE EXTERIOR ANGLES ARE
  CONGRUENT

11
PERPENDICULAR TRANSVERSAL THEOREM

• IF A TRANSVERSAL IS PERPENDICULAR TO ONE OF THE 2
  PARALLEL LINES, THEN IT IS PERPENDICULAR TO THE
  OTHER.