Download Guided Notes: Special Angle Pairs Date_________________ 1

Guided Notes: Special Angle Pairs
Date_________________
1. Angle parts: side, vertex, interior, exterior
2. __Adjacent Angles_____________: Two _coplanar_________ angles with a common __side____ and a
common _vertex______ but no common __interior points________.
(draw picture here)
3. __vertical angles_________: Two angles whose __sides_____ form 2 pairs of
___opposite rays___ - Look for intersection of 2 lines, X__.
(draw picture here)
4. __Complementary Angles___________: Two angles whose _measures______have a _sum __ of _90___
May be in right angle, or may not be adjacent_.
5. _Supplementary Angles____: Two angles whose _measures____have a _sum ___ of __180____.
6. __Linear Pair_________________: Two adjacent angles whose __non-common________sides are
__opposite rays______________. (Together they form a __straight angle_________ or a _line__.)
Angles in a linear pair are supplementary.
(draw picture here)
7. Identify pairs of angles that are:
1. Supplementary:  4 and  5
Or  3 and  4
2. Vertical:  3 and  5
3. Adjacent: answers will vary
4. Complementary:  2 and  3
or  2 and  5
5. linear pair:  4 and  5
Or  3 and  4
2
1
5
3
4
8. _Linear Pair Postulate______: Linear pairs of angles are _supplementary___________.
9. _Theorem___: a statement that has been __proven true_______________.
Theorem 1: Vertical angles are congruent_______________.
Theorem 2: If two angles are supplements (complements) or the same angle or of congruent angles, then
the two angles are congruent___.
. Theorem 3: All right angles are congruent______________________________.
. Theorem 4: If two angles are congruent and supplementary, then each is a right angle____________.
10. What are we allowed to conclude from a diagram?
o We CAN conclude information based on _diagrams_______:
 Adjacent angles
 Linear pairs of angles
 Vertical angles
 Addition postulates (angles and segments)
 Collinearity
 Information that is marked in the diagram
o We CANNOT conclude information based on _ diagrams _ UNLESS it is explicitly marked in the
diagram or stated in the directions/given information.
 Congruent (  ) angles or segments
 Right angles
 Whether lines are perpendicular or parallel
 Midpoints of bisectors
What conclusion can be made from the diagram at the right?






1  2, by the markings
2 and 3 are adjacent angles (for example)
4 and 5 are adjacent supplementary angles
(for example)
m4  m5  180 by the Angle Addition Postulate
1 and 4 are vertical pairs (for example)
Students may come up with others
4
3
5
2
1
Is it correct to make the given conclusion from the diagram at the right?
T
a. TW  WV yes, the congruent segs. are marked
b. QW  WP No, there are no markings
P
W
Q
c. TV  PQ No, there are no markings
d. TV bi sec ts PQ No, there are no markings
V
e. W is the midpoint of TV . Yes, the congruent segs. are marked
13. Vertical Angles:
a.
Find the value of x. 35
(4x)°
b. Find the measures of the labeled pair of vertical angles in the diagram. 140
c. Find the measure of the other pair of vertical angles. 40
(3x+35)°
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