The (Ultimate) Geometry Review Sheet Page 6
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15PARALLEL LINES
Make sure you know how to identify the different types of angles formed when two lines are cut by a
transversal:
The angle pairs {2, 8} and {3, 7} are alternate interior
angles—you can remember this because they form a sort of
“Z” shape or reversed “Z” shape.
The angle pairs {1, 2}, {4, 7}, {5, 8}, and {3, 6} are
corresponding angles—you can remember these because
they form a sort of “F” shape—whether upside-down,
reversed, or both!
The angle pairs {1, 5} and {4, 6} are alternate exterior
angles.
These lines are only parallel if:
alternate interior angles are congruent
alternate exterior angles are congruent
corresponding angles are congruent
same side interior angles are supplementary.
If you’re uncomfortable with those terms, you can visit:
for more information.
You can get some practice with solving for angles of parallel lines with this video:
Or:
(These are more traditional,
practice-like problems.)
CONGRUENT TRIANGLES
SSS Postulate - If two triangles have three pairs of corresponding sides that are congruent,
then the triangles are congruent.
SAS Postulate - Triangles are congruent if any pair of corresponding sides and their included
angles are congruent in both triangles.
ASA Postulate - Triangles are congruent if any two angles and their included side are
congruent in both triangles.
Hyp. Leg Theorem - Two right triangles are congruent if the hypotenuse and one
corresponding leg are congruent in both triangles.
AAS Theorem - Triangles are congruent if two pairs of corresponding angles and a pair of
non-included sides are equal in both triangles.
Corresponding sides of congruent triangles are congruent.
Isosceles Triangle Theorem - If two sides of a triangle are congruent, then the angles
opposite those sides are congruent.
Converse of the Isosceles Triangle Theorem - If two angles of a triangle are congruent, then
sides opposite those angles are congruent.
If a triangle is equiangular, then it is equilateral.
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