Chapter 4 Theorems
Corresponding parts of congruent triangles are congruent.
Postulate 12
SSS Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the
triangles are congruent.
Postulate 13
SAS Postulate
If tw
o sides and the included angle of one triangle are congruent to two sides and the
included angle of another triangle, then the triangles are congruent.
Postulate 14
ASA Postulate
If two angles and the included side of one triangle are congruent to two a
ngles and the
included side of another triangle, then the triangles are congruent.
Theorem 4
–
1
The Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are
congruent.
Corollary
An equilateral trian
gle is also equiangular
Corollary
An equilateral triangle has three 60 angles.
Corollary
The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at it’s
midpoint.
Theorem 4
–
2
If two angles of one triangle are congruen
t, then the sides opposite those angles are
congruent.
Corollary
An equiangular triangle is also equilateral
Theorem 4
–
3
AAS Theorem
If two angles and a non

included side of one triangle are congruent to the corresponding
parts of another triangle,
then the triangles are congruent.
Theorem 4
–
4
HL Theorem
If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts
of another right triangle, then the triangles are congruent.
Theorem 4
–
5
If a point lies on the pe
rpendicular bisector of a segment, then the point is equidistant
from the endpoints of the segment.
Theorem 4
–
6
If a point is equidistant from the endpoints of a segment, then the point lies on the
perpendicular bisector of the segment.
Theorem 4
–
7
If a point lies on the bisector of an angle, then the point is equidistant from the sides of
the angle.
Theorem 4
–
8
If a point is equidistant from the sides of an angle, then the point lies on the bisector of an
angle.
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