Question

h t t p : / / i m g 3 5 . i m a g e s h a c k . u s / i m g 3 5 / 8 0 8 7 / 4 7 2 4 1 4 6 9 . j p g

my book says

if a1 is perpendicular to a2 and b1 is perpeindicular to b2 then angle one equal angle two

WHY????

Also I remeber it was very simple but don't remeber why... if we exten lines a2 and b2 then angle two equals angle 3

WHY???

Please provide me with the reasons...

Thanks

Answer 1

I see two right-angled triangles in which opposite angles are also equal.

So if two angles of one triangle are equal to two angles of another triangle then the third angle pair must also be equal.
"sum of angles in a triangle theorem"

Answer 2

what are these opposite angles that you are making reference to sorry it's been a while sense I took geometry

Answer 3

draw any two intersecting straight lines.

Do you see two pairs of opposing or "opposite" angles?
Aren't they equal ?

Answer 4

Opposite angles are equal because each of those angles is supplementary to a common angle.

A+B=180
A+C=180

B must =C

Answer 5

oh and also what makes angle three equal to angle to if you extended the lines

Answer 6

Those will be opposite angles (if two lines intersect, then opposite angles are equal)