Download 1.1 Angle Pair Relations

November 11, 2015
1.1 Angle Pair Relations
November 11, 2015
straight angle an angle that is also a straight line, has a measure of 180o
linear pair a pair of angles that make a line; 2 angles that are adjacent and
supplementary
adjacent angles 2 angles that share a common side or ray have a
common vertex, and no interior points in common
supplementary angles 2 angles whose measures have a sum of 180o
40o
140o
*Note: All linear pairs are supplementary angles, but not all supplementary
angles are linear pairs!!
November 11, 2015
vertical angles 2 nonadjacent (opposite) angles formed by two intersecting lines
interior angles angles formed on the inside of two lines cut by a transversal
exterior angles angles formed on the outside of two lines cut by a transversal
EXTERIOR
INTERIOR
EXTERIOR
November 11, 2015
parallel two or more lines on a flat surface that do
not intersect (no matter how far they extend)
>>
>>
Arrowheads at the end of lines
indicate that they extend
indefinitely. Marks on pairs of
lines or segments like > and >>
indicate that the lines are parallel.
perpendicular two lines or segments that meet (intersect) to
form a 90o angle
The small box at the point of
intersection of two lines or
segments indicates that they are
perpendicular (form right angles)
transversal a line that intersects
two or more lines
r and w are
transversals
November 11, 2015
corresponding angles a pair of angles that are in the same "corresponding" location
relative to the parallel line and transversal . . .
angles on the same side to their respective parallel line and on
the same side of the transversal
conjecture - (an inference based on incomplete evidence)
If two parallel lines are cut by a transversal, then the
corresponding angles are . . .
November 11, 2015
alternate interior angles a pair of angles that are on the inside of the parallel lines and
opposite sides of the transversal . . .
conjecture - (an inference based on incomplete evidence)
If two parallel lines are cut by a transversal, then the alternate
interior angles are . . .
November 11, 2015
consecutive interior angles a pair of angles that are on the inside of the parallel lines and
same side of the transversal . . .
aka. same side interior angles
conjecture - (an inference based on incomplete evidence)
If two parallel lines are cut by a transversal, then the
consecutive interior angles are . . .
November 11, 2015
Classify each of the following pairs of angles as corresponding,
alternate interior, same side interior, straight, or "none" of these.
What conditions are necessary to be able to say that the pairs of
corresponding angles or alternate interior angles are congruent?
If m<2 = 670, what is m<5?
If m<4 = 6x0 and ,<6 = 9x0, find the m<4.
Explain your steps.
November 11, 2015
Use all that you now know, lets make some more comparisons.
Compare the measures of angles e and x.
x
Compare the measures of angles a and e.
Compare m<f and m<y.
Compare m<f and m<k.
y
Compare m<n and m<z.
z
Compare m<n and m<t.
November 11, 2015
alternate exterior angles a pair of angles that are on the outside of the parallel lines and
opposite sides of the transversal . . .
conjecture If two parallel lines are cut by a transversal,
then the alternate exterior angles are . . .
consecutive exterior angles a pair of angles that are on the outside of the parallel lines and
same side of the transversal . . .
aka. same side exterior angles
conjecture If two parallel lines are cut by a transversal,
then the consecutive exterior angles are . . .
November 11, 2015
Use your conjectures about parallel lines and the angles formed by the transversal to
find the measures of the labeled angles. Show the step by step procedure you use and
name each angles conjecture you use.
November 11, 2015
Learning Log
a) Label each diagram below with the name of the angle pair that best describes it.
b)Describe the angle pair using your geometry vocabulary.
c) State the conjecture for the angle pair.
linear pair -
supplementary
a pair of angles that make a line; 2 angles that are
adjacent (side by side - share a side) and
supplementary (sum of 1800)
congruent
vertical angles 2 nonadjacent (opposite) angles formed by
two intersecting lines
corresponding angles -
congruent
a pair of angles that are in the same "corresponding"
location relative to the parallel line and transversal . . .
angles on the same side to their respective parallel line
and on the same side of the transversal
alternate interior angles -
congruent
a pair of angles that are on the inside of the parallel
lines and opposite sides of the transversal . . .
alternate exterior angles -
congruent
a pair of angles that are on the outside of the parallel
lines and opposite sides of the transversal . . .
consecutive interior angles -
supplementary
a pair of angles that are on the inside of the parallel lines
and same side of the transversal . . .
aka. same side interior angles
consecutive exterior angles -
supplementary
a pair of angles that are on the outside of the parallel lines
and same side of the transversal . . .
aka. same side exterior angles
November 11, 2015
1.1 Angle Pair Relations
November 11, 2015
straight angle an angle that is also a straight line, has a measure of 180o
linear pair a pair of angles that make a line; 2 angles that are adjacent and
supplementary
adjacent angles 2 angles that share a common side or ray have a
common vertex, and no interior points in common
supplementary angles 2 angles whose measures have a sum of 180o
40o
140o
*Note: All linear pairs are supplementary angles, but not all supplementary
angles are linear pairs!!
November 11, 2015
vertical angles 2 nonadjacent (opposite) angles formed by two intersecting lines
interior angles angles formed on the inside of two lines cut by a transversal
exterior angles angles formed on the outside of two lines cut by a transversal
EXTERIOR
INTERIOR
EXTERIOR
November 11, 2015
parallel two or more lines on a flat surface that do
not intersect (no matter how far they extend)
>>
>>
Arrowheads at the end of lines
indicate that they extend
indefinitely. Marks on pairs of
lines or segments like > and >>
indicate that the lines are parallel.
perpendicular two lines or segments that meet (intersect) to
form a 90o angle
The small box at the point of
intersection of two lines or
segments indicates that they are
perpendicular (form right angles)
transversal a line that intersects
two or more lines
r and w are
transversals
November 11, 2015
a)Take a sheet of patty paper and place it over angle a. Using a ruler
as a guide, make a precise copy of the angle and label it. Slide the
copy of <a to <c and compare the sizes of the two angles. What do
you observe?
b)Trace a copy of <b. Slide it to <d and compare. What do you
observe?
c)Trace a copy of <e. Slide it to <g and compare. What do you
observe?
d)Trace a copy of <f. Slide it to <h and compare. What do you
observe?
e) Both figures show two lines that are intersected by a transversal.
Summarize your findings by describing the relationship between pairs
of angles created by lines cut by a transversal.
When the angles are congruent, what must be true about the two
intersected lines?
If the lines are parallel, then what must be true about the angles?
November 11, 2015
Use what you know about straight angles and vertical angles to find the
measures of missing angles b and d, f and k, and r and s. Label each
angle with its measurement. Be prepared to explain your thinking.
Compare the measures of angles a and d,
and then compare the measures of angles
b and e.
Compare the measures of angles f and j,
and then compare the measures of angles
g and k.
Compare the measures of
angles t and r, and then
compare the measures of
angles n and s.
November 11, 2015
corresponding angles a pair of angles that are in the same "corresponding" location
relative to the parallel line and transversal . . .
angles on the same side to their respective parallel line and on
the same side of the transversal
conjecture - (an inference based on incomplete evidence)
If two parallel lines are cut by a transversal, then the
corresponding angles are . . .
November 11, 2015
Use what you know about straight angles, vertical angles, and what you
learned from the previous example to find the measures of angles c, h
and w.
Compare the measures of angles c and d.
Compare m<h and m<j.
Compare m<w and m<s.
November 11, 2015
alternate interior angles a pair of angles that are on the inside of the parallel lines and
opposite sides of the transversal . . .
conjecture - (an inference based on incomplete evidence)
If two parallel lines are cut by a transversal, then the alternate
interior angles are . . .
November 11, 2015
Use all that you now know, lets make some more comparisons.
Compare the measures of angles b and d.
Compare m<g and m<j.
Compare m<r and m<s.
November 11, 2015
consecutive interior angles a pair of angles that are on the inside of the parallel lines and
same side of the transversal . . .
aka. same side interior angles
conjecture - (an inference based on incomplete evidence)
If two parallel lines are cut by a transversal, then the
consecutive interior angles are . . .
November 11, 2015
Classify each of the following pairs of angles as corresponding,
alternate interior, same side interior, straight, or "none" of these.
What conditions are necessary to be able to say that the pairs of
corresponding angles or alternate interior angles are congruent?
If m<2 = 670, what is m<5?
If m<4 = 6x0 and ,<6 = 9x0, find the m<4.
Explain your steps.
November 11, 2015
Use all that you now know, lets make some more comparisons.
Compare the measures of angles e and x.
x
Compare the measures of angles a and e.
Compare m<f and m<y.
Compare m<f and m<k.
y
Compare m<n and m<z.
z
Compare m<n and m<t.
November 11, 2015
alternate exterior angles a pair of angles that are on the outside of the parallel lines and
opposite sides of the transversal . . .
conjecture If two parallel lines are cut by a transversal,
then the alternate exterior angles are . . .
consecutive exterior angles a pair of angles that are on the outside of the parallel lines and
same side of the transversal . . .
aka. same side exterior angles
conjecture If two parallel lines are cut by a transversal,
then the consecutive exterior angles are . . .
November 11, 2015
Use your conjectures about parallel lines and the angles formed by the transversal to
find the measures of the labeled angles. Show the step by step procedure you use and
name each angles conjecture you use.
November 11, 2015
Learning Log
a) Label each diagram below with the name of the angle pair that best describes it.
b)Describe the angle pair using your geometry vocabulary.
c) State the conjecture for the angle pair.
November 11, 2015
Learning Log
a) Label each diagram below with the name of the angle pair that best describes it.
b)Describe the angle pair using your geometry vocabulary.
c) State the conjecture for the angle pair.
linear pair -
supplementary
a pair of angles that make a line; 2 angles that are
adjacent (side by side - share a side) and
supplementary (sum of 1800)
congruent
vertical angles 2 nonadjacent (opposite) angles formed by
two intersecting lines
corresponding angles -
congruent
a pair of angles that are in the same "corresponding"
location relative to the parallel line and transversal . . .
angles on the same side to their respective parallel line
and on the same side of the transversal
alternate interior angles -
congruent
a pair of angles that are on the inside of the parallel
lines and opposite sides of the transversal . . .
alternate exterior angles -
congruent
a pair of angles that are on the outside of the parallel
lines and opposite sides of the transversal . . .
consecutive interior angles -
supplementary
a pair of angles that are on the inside of the parallel lines
and same side of the transversal . . .
aka. same side interior angles
consecutive exterior angles -
supplementary
a pair of angles that are on the outside of the parallel lines
and same side of the transversal . . .
aka. same side exterior angles
November 11, 2015
Find the measure of each angle below. Justify your answer by naming the angle pair conjecture used.
86o
V
V
a
c
128o
i
j
f
d
b
e
g
h
k
l
November 11, 2015
b
d
c 59o
f g
e
i
k l
p q
h
j
43o
m
r
n
s
V
a
V
Find the measure of each angle below. Justify your answer by naming the angle pair conjecture used.
November 11, 2015