1. Congruent angles
are angles that have the same number of degrees. For instance, 2 line
segments are congurent if they are the same in length. If
two angles have the same
measure, they too are considered congruent. Symbolically, this can be
shown by: as
Line Segment AB is congruent to line segment OP
refers to the line, ray or line segment that passes through the midpoint.
The bisector divides a segment into two congruent setments as demonstrated
A ray that
is in the interior of an angle and divides the original angle into two
congruent angles is the bisector of that angle.
and Interior Angles
is a line that crosses two parallel lines. In the figure below, A and
B are parallel lines. Note the following when a transversal cuts two
*the four acute angles will be equal
*the four obtuse angles will also be equal
*each acute angle is supplementary to eacy obtuse angle
5. 3 Theorems
to Know - Especially for your SATs!
sum of the measures of triangles always equals 180°. You can prove
this by using your protractor to measure the three angles, then total
the three angles. See triangle below - 90° + 45° + 45° =
measure of the exterior angle will always equal the sum of the measure
of the 2 remote interior angles. NOTE: the remote angles in the
figure below are
b and c.
Therefore, the measure of
RAB will be equal to the sum of
B and C.
If you know the measures
B and C
then you automatically know what
3. If a
transversal intersects two lines such that corresponding angles are
congruent, then the lines are parallel. AND, If two lines are intersected
by a transversal such that interior angles on the same side of the transversal
are supplementary, then the lines are parallel. (See above Transversal)