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04/20/23 1.7: Angle Relationships
1-7: Angle 1-7: Angle Relationships Relationships
1-7: Angle 1-7: Angle Relationships Relationships
Expectations:Expectations:1.1.You will be able to solve problems involving You will be able to solve problems involving
congruent and supplementary angles.congruent and supplementary angles.2.2.You will be able to explain the difference You will be able to explain the difference
between adjacent angles and linear pairs of between adjacent angles and linear pairs of angles.angles.
3.3.You will be able to use the linear pair You will be able to use the linear pair postulate and the vertical angle theorem to postulate and the vertical angle theorem to
solve problems.solve problems.
Do you remember …
1. Complementary angles2. Supplementary angles3. Perpendicular lines
04/20/23 1.7: Angle Relationships
04/20/23 1.7: Angle Relationships
Complementary Angles
Defn: Two angles are complementary iff the sum of their measures is ____.90
04/20/23 1.7: Angle Relationships
Angle A is complementary to angle B. If m∠B is 3 less than twice m∠A, what are m∠A and m∠B?
04/20/23 1.7: Angle Relationships
Supplementary Angles
Defn: Two angles are supplementary iff the sum of their measures is ________.
04/20/23 1.7: Angle Relationships
Perpendicular LinesDefn: Two lines l and m are
perpendicular, written l ⊥m , iff they intersect to form ________________________.
l
m
Now some new terms.
04/20/23 1.7: Angle Relationships
04/20/23 1.7: Angle Relationships
Adjacent Angles
Defn: Two angles are adjacent iff they share a ___________________, but have no interior points in common.
04/20/23 1.7: Angle Relationships
1 2
Angles 1 and 2 are adjacent angles.
04/20/23 1.7: Angle Relationships
1
23
4Angles 1 and 3 (and 2 and 4) are not adjacent angles. Why?
04/20/23 1.7: Angle Relationships
A
B
C
D
∠ABC and ABD are not adjacent. Why?∠
In the figure below, which pairs of angles are adjacent angles?
A.∠2 and ∠ 3B.∠7 and ∠8C.∠4 and ∠5D.∠2 and ∠7E. ∠4 and ∠6
04/20/23 1.7: Angle Relationships
1
2
3
4
5 7
86
04/20/23 1.7: Angle Relationships
Linear PairDefn: Two adjacent angles form a
linear pair iff their non-common sides are _________________.
04/20/23 1.7: Angle Relationships
1 2
∠1 and 2 form a linear pair.∠
Draw a pair of adjacent angles that do not form a linear pair.
04/20/23 1.7: Angle Relationships
Geometers Sketch Pad “Linear Pairs.”
04/20/23 1.7: Angle Relationships
04/20/23 1.7: Angle Relationships
Linear Pair PostulateIf two angles form a linear pair, then they
are __________________.
04/20/23 1.7: Angle Relationships
Vertical AnglesDefn: Two angles are vertical angles iff
they are ______________ angles formed by two intersecting lines.
14
32
Quick “Quiz”
04/20/23 1.7: Angle Relationships
04/20/23 1.7: Angle Relationships
What type of angles are these?
1 2
04/20/23 1.7: Angle Relationships
What type of angles are these?
1
2
04/20/23 1.7: Angle Relationships
What type of angles are these?
1
2
04/20/23 1.7: Angle Relationships
Vertical Angles and Linear Pairs
Geometers Sketch Pad “Vertical Angles.”
04/20/23 1.7: Angle Relationships
Vertical Angle Theorem If two angles are vertical angles,
then they are ____________.
04/20/23 1.7: Angle Relationships
Determine whether the following are true or false:a. If 2 angles are supplementary, then they form a linear pair.b. If 2 angles form a linear pair, then they are supplementary.
04/20/23 1.7: Angle Relationships
What are the measures of all of the angles below?
1
3
2
4
04/20/23 1.7: Angle Relationships
Perpendicular Lines Theorem
Two Perpendicular lines form ___ right angles.
7 minute writeUsing geometrical terms and
complete sentences, tell me (in writing) why you know the Perpendicular Lines Theorem must be true.
This will be handed in and corrected for points.
04/20/23 1.7: Angle Relationships
04/20/23 1-7: Angle Relationships 31
Determine the measure of each angle if m∠1=5x+11 and m∠2=8x-1.
1 234
A. 31, 31B. 31, 59C. 31, 149D. 41.95, 48.25E. 76.4, 103.6
What is the difference of the measures of angles 1 and 2 in the diagram below if m∠1 = 8x + 4 and m∠2 = 12x – 8, rounded to the
nearest whole number?
A. 0B. 3C. 6D. 9E. 25
04/20/23 1-7: Angle Relationships 32
∠1∠2
04/20/23 1.7: Angle Relationships
Things you may assume from an unmarked
drawing collinear points, betweenness,
intersections, position of figures with relationship to one another, opposite rays, adjacent angles, linear pairs
These are really important!!!!
04/20/23 1.7: Angle Relationships
Things you should not assume from a drawing measures, perpendicular lines,
parallel lines, congruence, midpoints, bisectors, supplementary angles, complementary angles.
These are even more important!!!!!
04/20/23 1.7: Angle Relationships
Assignment pages 59,# 15 – 25 (odds), 29 and 31 andpages 111 – 112, # 22 – 32 (evens)
