Download 1.1 Angle Pair Relations

1.1 Angle Pair Relations
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!!
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
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
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.
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 . . .
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.
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 . . .
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.
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 . . .
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.