Download Unit 3 - Congruent Triangles - Theorem and Postulate Sheet

Unit 3 Congruent Triangles Theorem and Postulate Sheet
Theorem/Postulate/Formula
Name and/or Number
Actual Wording
Theorem 4.1 Properties of
Congruent Triangles
1. Every triangle is congruent to itself
2. If
, then
3. If
and
,
then
.
The sum of the measures of the interior
angles of a triangle is
If two angle of one triangle are congruent
to two angles of another triangle, then the
third angles are also congruent.
The acute angles of a right triangle are
complementary.
The measure of an exterior angle of a
triangle is equal to the sum of the
measures of the two remote
(nonadjacent) interior angles.
The measure of an exterior angle of a
triangle is greater than the measure of
either of the two remote (nonadjacent)
interior angles.
If three sides of one triangle are congruent
to three sides of a second triangle, then
the two triangles are congruent.
If two sides and the included angle of one
triangle are congruent to two sides and
the included angle of a second triangle,
then the two triangles are congruent.
Theorem 4.2 Triangle Sum
Theorem
Theorem 4.3 Third Angles
Theorem
Theorem 4.4
Theorem 4.5 Exterior Angle
Theorem
Theorem 4.6 Exterior Angle
Inequality
Postulate 17 Side-Side-Side
(SSS) Congruence Postulate
Postulate 18 Side-Angle-Side
(SAS) Congruence Postulate
Diagram/Example
In Your Own Words
Postulate 19 Angle-SideAngle (ASA) Congruence
Postulate
Theorem 4.7 Angle-AngleSide (AAS) Congruence
Postulate
Theorem 4.8 Base Angles
Theorem
Theorem 4.9
Corollary to Theorem 4.8
Corollary to Theorem 4.9
Theorem 4.10 HypotenuseLeg (HL) Congruence
Theorem
If two angles and the included side of one
triangle are congruent to two angles and
an included side of a second triangle, then
the triangles are congruent.
If two angles and a nonincluded side of
one triangle are congruent to two angles
and the corresponding nonincluded side of
a second triangle, then the two triangles
are congruent.
If two sides of a triangle are congruent,
then the angles opposite to them are
congruent.
If two angles of a triangle are congruent,
then the sides opposite to them are
congruent.
If a triangle is equilateral, then it is also
equiangular.
If a triangle is equiangular, then it is also
equilateral.
If the hypotenuse and a leg of a right
triangle are congruent to the hypotenuse
and leg of a second right triangle, then the
two triangles are congruent.