Transparency 5
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Transparency 5. Click the mouse button or press the Space Bar to display the answers. Transparency 5a. Lesson 1-5. Learners will be able to identify and use. special pairs of angles and perpendicular lines. Adjacent angles :. - PowerPoint PPT Presentation
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Lesson 1-5
are two angles that lie in the same plane, have a common
vertex, and a common side, but no common
interior points.
Adjacent angles:
are two nonadjacent angles formed by two
intersecting lines
Vertical angles:
is a pair of adjacent angles whose
noncommon sides are opposite rays.
Linear pair:
Name two angles that form a linear pair.
A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.
Answer: The angle pairs that satisfy this definition are
Name two acute vertical angles.
There are four acute angles shown. There is one pair of vertical angles.
Answer: The acute vertical angles are VZY and XZW.
Name an angle pair that satisfies each condition.
a. two acute vertical angles
b. two adjacent angles whose sum is less than 90
Answer: BAC and CAD or EAF and FAN
Answer: BAC and FAE, CAD and NAF, or BAD and NAE
are two angles whose measures have a sum
of 90.
Complementary angles:
are two angles whose measures have a sum
of 180.
Supplementary angles:
ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the other angle.
Explore The problem relates the measures of two supplementary angles. You know that the sum of the measures of supplementary angles is 180.
Plan Draw two figures to represent the angles.
Let the measure of one angle be x.
Solve
Given
Simplify.
Add 6 to each side.
Divide each side by 6.
Use the value of x to find each angle measure.
Examine Add the angle measures to verify that the angles are supplementary.
Answer: 31, 149
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
intersect to form four right angles.
Intersect to form congruent
adjacent angles.Is read is perpendicular to
Perpendicular lines:
ALGEBRA Find x so that .
If , then mKJH 90. To find x, use KJI and IJH.
Substitution
Add.
Subtract 6 from each side.
Divide each side by 12.
Answer:
Sum of parts whole
ALGEBRA Find x and y so that and are perpendicular.
Answer:
The diagram is marked to show that From the definition of perpendicular, perpendicular lines intersect to form congruent adjacent angles.
Answer: Yes; and are perpendicular.
Determine whether the following statement can be assumed from the figure below. Explain.
mVYT = 90
Determine whether the following statement can be assumed from the figure below. Explain.
TYW and TYU are supplementary.
Answer: Yes; they form a linear pair of angles.
Determine whether the following statement can be assumed from the figure below. Explain.
VYW and TYS are adjacent angles.
Answer: No; they do not share a common side.
Determine whether each statement can be assumed from the figure below. Explain.
a.
b. TAU and UAY are complementary.
c. UAX and UXA are adjacent.
Answer: Yes; lines TY and SX are perpendicular.
Answer: No; they do not share a common side.
Answer: No; the sum of the two angles is 180, not 90.
Homework:Lesson 1-5, p. 41
# 8-22,24-34 even,
41, 43
