Transcript Angle Relationships

Angle Relationships
Adjacent - Two angles are adjacent if and
only if they satisfy four conditions:
1. They lie in the same plane.
2. They have a common vertex.
3. They have a common side.
4. They have no common interior points.
Angle Relationships
Vertical angles - Two nonadjacent angles
formed by two intersecting lines. All
vertical angles are congruent.
Linear Pair - A pair of adjacent angles whose
noncommon sides are opposite rays. The
angles in a linear pair have measures that
add to 180 degrees.
Name an angle pair that satisfies each condition.
a. two acute vertical angles
Answer: BAC and FAE,
CAD and NAF, or
BAD and NAE
b. two adjacent angles whose
sum is less than 90
Answer: BAC and CAD or
EAF and FAN
Angle Relationships
Complementary Angles - Two angles whose
measures have a sum of 90 degrees.
Supplementary Angles - Two angles whose
measures have a sum of 180 degrees.
ALGEBRA Find the measures of two complementary
angles if one angle measures six degrees less than
five times the measure of the other.
Answer: 16, 74
Angle Relationships
Perpendicular () - Lines that intersect to form
right angles.
• Perpendicular lines intersect to form four right
angles.
• Perpendicular lines intersect to form congruent
adjacent angles.
• Segments and rays can be perpendicular to lines or
to other line segments and rays.
• The right angle symbol in a figure indicates that
the lines are perpendicular.
ALGEBRA Find x and y so that
are perpendicular.
Answer:
and
Determine whether each statement can be assumed
from the figure below. Explain.
a.
Answer: Yes; lines TY and SX
are perpendicular.
b. TAU and UAY are
complementary.
Answer: No; the sum of the
two angles is 180, not 90.
c. UAX and UXA are adjacent.
Answer: No; they do not share
a common side.