1. H G Given cube
E F ABCD.EFGH with
the length of edge
is 4 cm. Determine
the distance of :
D C
A 4 cm B
a.Line AB to line HG
b.Line AD to line HF
c.Line BD to line EG
1

2. Solution
H G
The distance of line:
E a. AB to line HG
F
= AH (AH  AB,
AH  HG)
D C = 4√2 (side diagonal)
A 4 cm B b.AD to line HF
= DH (DH  AD,
DH  HF
= 4 cm
2

3. H Q G The distance of line:
E F b.BD to line EG
= PQ (PQ  BD,
D C PQ  EG
A P = AE
4 cm B
= 4 cm
3

4. Projection of line to plane
We can make the
A projection of line to plane
B by projection some
g points in the line to
plane.
A’ g’
B’
So, the projection of line g to the plane
H is g’
4

5. Example 1
H G
E
Given cube
F
ABCD.EFGH
a. The projection of line
D
EF to plane ABCD
C is….
A B
b. If the length of edge is 6 cm,
The length of projection line CG
to plane BDG is ….
5

6. Solution :
H G
E
a. The projection of line
F EF to the plane
ABCD is determining
the projection of point
D C E and F to the plane
A B ABCD, they are point
A and B.
So, the projection of line EF to the
plane ABCD is line AB.
6

7. b. The projection of line
H G CG to plane BDG is
E F determining the
projection of point C
P and G to plane BDG,
D
they are point P and
C G.
A 6 cm B
So, the projection of line CG to
plane BDG is line PG.
7

8. H G •The length of PG is:
E F
•PG = ⅔.GR
P = ⅔.½a√6
D C
A
R
B
= ⅓a√6 = ⅓.6√6
6 cm
•So, the length of projection from
line CG to plane BDG is 2√6 cm
8

9. Example 2
Given regular pyramid
T T.ABCD with the length
of AB= 16 cm, TA = 18
cm.
The length of projection
D C TA to plane ABCD is ….
A 16 cm B
9

10. Solution
Projection of TA to
T plane ABCD is AT’.
Length of AT’= ½AC
= ½.16√2
D C = 8√2
T’
A 16 cm B
So, the length of projection from line
TA to plane ABCD is 8√2 cm
10

11. Activities class
1. Given the cube ABCD.EFGH with the length of
edge is 6 cm. Determine the length of
projection from line AG to :
a.Plane ABCD
b.Plane ADHE
c.If M is the cut point from side diagonals in
plane ABCD. The length of projection from
line GM to plane BCGF is …