-2.4- (Angles/Perpendicular Lines & Theorems)

Today (Tuesday) we had a short lesson about complementary and supplementary angles.

Definitions:

Complementary Angles - Two angles that sum up to 90 degrees.
(THE ABOVE ANGLES NEED NOT BE ADJACENT)

Example:

Supplementary Angles (Straight Line) - Two angles that sum up to 180 degrees.
(THE ABOVE ANGLES NEED NOT BE ADJACENT)

Example:

Vertical Angles - Angles formed by the intersection of two lines or segments. The angles are located opposite of each other. They are always congruent.

Example:


Angles 1 and 2 (blue) are congruent to each other.
Angles 3 and 4 (red) are congruent to each other.









General Examples:

1)

Given: A(2) is congruent to A(3).
Ask: Is A(1) congruent to A(4)?


Proof:
A(2) is congruent A(3)
and A(2) is congruent to A(4)
since A(3) is congruent to A(4) (vert. angles).

A(2) is congruent to A(1) (vert. angles)
and is also congruent to A(4), therefore,
A(1) is congruent to A(4).


2)
Solve)
3x - 66 = x
2x = 66
x = 33

Is the line perpendicular?)

(3x = 99)

3x - 66 = 33
50 + 33 = 83

It is not a right angle, therefore, the line is NOT perpendicular.



SO, WHO IS THE NEXT SCRIBE?
The next scribe is . . .







PHIL K. >:D