Download Vertical Angles

“Education is our passport to the future, for
tomorrow belongs to the people who prepare
for it today.”
― Malcolm X
Do Now
Put your 2.5 worksheet on your desk ready to be
stamped.
Take a protractor from the front.
Take out your compass.
Write down the linear pairs conjecture
Write down the vertical angles conjecture
Parallel Lines and
Transversals
Parallel Lines
Two lines are said to be parallel if
(i) they both lie in the same plane, and,
(ii) they do not intersect (or cross each other)
Transversal
A third line that crosses a pair of parallel lines on a
slant
As the transversal crosses the two parallel lines, eight
angles are formed
Draw this in your notes
∠1 = ∠3 = ∠5 = ∠7
and
∠2 = ∠4 = ∠6 = ∠8
Linear Pairs
Pairs of adjacent angles are supplementary (always
add up to 180o) , as you can see from the figure.
Thus ∠ 1 + ∠ 2 = 180o , ∠ 2 + ∠ 3 = 180o , ∠ 3 + ∠ 4 = 180o
, ∠ 5 + ∠ 6 = 180o , etc.
Corresponding Angles
Angles in the same relative position around the two
intersection points are called corresponding angles .
Thus ∠ 1 and ∠ 5 are corresponding angles, as are ∠ 4
and ∠ 8,
∠ 2 and ∠ 6, and also ∠ 3 and ∠ 7.
Corresponding angles are congruent (same angle
measure).
Alternate Interior
Angles
Alternate sides of the transversal
Inside the parallel lines
∠3 and ∠5 are called alternate interior angles.
and ∠6 are also alternate interior angles.
Alternate interior angles are congruent.
∠4
Alternate Exterior
Angles
Alternate sides of the transversal
Outside the parallel lines
∠2 and ∠8 are called alternate exterior angles.
and ∠7 are also alternate exterior angles.
Alternate exterior angles are congruent.
∠1
Vertical Angles
When two lines cross they form four angles.
∠ 1 and ∠ 3 are said to be vertical angles
∠ 2 and ∠ 4 also form vertical angles.
Vertical angles are congruent.
Thus ∠ 1 = ∠ 3 and
∠2=∠4
Determine the values of angles A, B, C,
and D, in the figure below. Assume that
the horizontal lines are parallel.
Exit Slip
1. Give a counterexample to this statement: “If two
angles are supplementary, then they are congruent.”
2. Use the diagram at
the right
•
•
•
Find m<1+m<2.
Find m<4.
Find m<3+m<4.
3. Name the relationship between <1 and <4.
4. Name the relationship between <1 and <2.