Download 11-1 Angle and Line Relationships

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3/9/17
11-1 ​Angle and Line Relationships
I can ​examine relationships between pairs of angles.​ I can ​examine
relationships of angles formed by parallel lines and a transversal.
REVIEW​:
Basic Definitions:
Ray​ – a part of a line that starts at one endpoint and extends forever.
Angle ​– is formed by two rays with a common endpoint – Vertex.
Congruent​ – same shape and size.
Degrees​ – units for angle measures.
Types of Angles:
1. Right angle – measures exactly 90°
2. Acute angle – measures less than 90°
3. Obtuse angle – measures more than 90° and less than 180°
4. Straight angle – measures exactly 180°
Naming Angles: ​Use an angle symbol with ​three​ capital letters. Vertex
must be in the middle.
PAIRS OF ANGLES
1. Vertical Angles
2. Adjacent Angles
3. Complementary Angles
4. Supplementary Angles
a pair (two angles) of opposite
congruent angles formed by
intersecting lines.
Two angles whose measures add to 90°
A pair of angles that share a common
ray (side) and a vertex.
Two angles whose measures add to 180°
LINES
1. Perpendicular lines – lines in a plane that
intersect to form four right angles
2. Parallel lines – lines in a plane that do not
intersect
3. Transversal line – a line that intersects two parallel lines
SPECIAL ANGLE RELATIONSHIPS ​(nonadjacent angles)
1. Alternate Exterior Angles – angles
that are on opposite sides of the
transversal and outside the parallel
lines
2. Alternate Interior Angles – angles
that are on opposite sides of the
transversal and inside the parallel
lines
3. Corresponding Angles – angles that
are in the same position on the parallel
lines in relation to the transversal
EXAMPLE 1.​ Name the angle in four ways
EXAMPLE 2.​ Classify the pairs of angles shown. Then find the value
of x in each figure.
A)
B)
C)
EXAMPLE 3.​ In the figure at the right, r ǁs and w is a transversal. If
m ∠1 = 128°, find the measure of each angle. Explain your reasoning.
EXAMPLE 4.​ If m ∠ABD = 164°, find m ∠ABC and m ∠CBD.
Homework:
GPA page 622 (10-32 all)