The document discusses properties of transversals and parallel lines. It shows examples of parallel lines cut by a transversal and defines the ratio of intercepts theorem - that the ratio of corresponding intercepts of parallel lines cut by a transversal is equal. An example problem demonstrates using the ratio of intercepts theorem to find the length of an unknown intercept given the other intercept lengths.

1. Properties of
Transversals

2. Properties of
Transversals

3. Properties of
Transversals
A
B
C

4. Properties of
Transversals
P
Q
A R
B
C

5. Properties of
Transversals
X
Y
P
Q Z
A R
B
C

6. Properties of
Transversals
X
Y
P
Q Z
A R
B
C
AB PQ XY
  ratio of intercepts of || lines
BC QR YZ

7. Properties of
TransversalsX 6 cm
Y x cm
P
Q Z
A R
B
2 cm C
3 cm
AB PQ XY
  ratio of intercepts of || lines
BC QR YZ

8. Properties of
TransversalsX 6 cm
Y x cm
P
Q Z
A R
B
2 cm C
3 cm
AB PQ XY
  ratio of intercepts of || lines
BC QR YZ
2 6

3 x

9. Properties of
Transversals X
6 cm
Y
P x cm
Q Z
A R
B
2 cm C
3 cm
AB PQ XY
  ratio of intercepts of || lines
BC QR YZ
2 6

3 x
2 x  18
x9

10. Exercise 8I; 1 to 6 ac etc, 9, 10b, 12, 16