Download Triangle Congruence

Triangle Congruence
Two plane figures are congruent if and only if one can be obtained from the other by rigid
motions. The symbol for congruent is ≅
Corresponding Parts of Congruent Triangles are Congruent Theorem (CPCTC)- if two
triangles are congruent, then corresponding sides and corresponding angles are congruent.
Side Side Side postulate states that if three sides of one triangle are congruent to three
sides of another triangle, then these two triangles are congruent.
Angle Side Angle Postulate states that if two angles and the included side of one triangle
are congruent to the corresponding parts of another triangle, the triangles are congruent.
Side Angle Side postulate states that if the two sides and the included angle of one triangle
are congruent to the corresponding parts of another triangle, they are congruent.
Angle Angle Side states that if two angles and the non-included side of one triangle are
congruent to the corresponding parts of another triangle, the triangles are congruent.
Hypotenuse Leg Theorem states that if the hypotenuse and leg of one triangle are
congruent to the corresponding parts of another right triangle, the right triangles are
congruent.
Side lengths that are congruent are represented with “tick” marks. These are short lines
drawn perpendicular to the side length. If one side has one “tick” mark on one triangle and a
side on another triangle, then those two sides are congruent.
Angles measures that are congruent are represented with angle markers. These are curved
lines inside of the angles. Angle markers work just like “tick” marks. If there is an angle on
one triangle that has two angle markers in one angle, and there is another triangle that has
two angle markers in one angle, then those two angles are congruent.
Examples of Identifying Congruence between two triangles.
From the practice packet.
# 1. You are given one pair of congruent angles, and one congruent side from the figure.
You can draw another pair of congruent angles from the vertical angle. There are two
angles that are congruent and a non-included sided, therefore these triangles are congruent
by Angle Angle Side.
# 7. You are given two pairs of congruent corresponding angles and the two triangles share
a side, therefore that side is congruent to itself for each triangle. The two angles and their
included side are congruent, therefore the triangles are congruent. The included side is
between the corresponding congruent angles, so the two triangles are congruent using
Angle Side Angle.