Title: Vertically opposite angles are equal
1NON - PARALLEL LINES
Try example
Vertically opposite angles are equal
2Corresponding angles
3With parallel lines
corresponding angles are equal
4Alternate angles
5With parallel lines
alternate angles are equal
Try example
6A triangle has three angles
Try example
See proof
Angles in a triangle add up to 180o
7Example Find angles r, s t
137 o
t
s
r
8 r 137o (vertically opposite angles) s
43o (Angles on a straight line) t 43o (Angles
on a straight line or vertically opposite angles)
Solution
137 o
t
s
r
9Example Find angles a, b c
a
73o
b
c
10a 73o (vertically opposite angles) b
73o Alternate angles c 73o (corresponding
angles) d 107o (angles on straight line)
Solution
a
73o
b
c
d
1135o
Examples Find angle m Find angle n
n
57o
44o
m
12m 180 - (44 35) 180 - 79 101o n
180 - (90 57) 180 - 147 33o
35o
n
57o
44o
m
13The triangle has three angles
Alternate angles on parallel lines are equal
The three angles make a straight line. They add
up to 180o
Hence, angles in a triangle add up to 180o
14Alternate angles
Another Proof
Corresponding angles
Three angles in a triangle
15THE END