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Chapter 4
Congruency
• Congruent Figures – figures that have
exactly the same size and shape.
To check for congruency, you may have to
slide, flip, or turn.
• Online: Flip, slide and turn…
• CPCTC: Corresponding Parts of
Congruent Triangles are Congruent.
Two triangles are congruent if and only if
ALL their corresponding parts are congruent.
However, we do not have to measure every
single part of a triangle to determine if they are
congruent…
WE CAN USE OUR TRIANGLE POSTULATES!
Side–Side–Side Postulate (SSS)
• If three sides of one triangle are
congruent to three sides of another
triangle, then the triangles are
congruent.
Side–Angle–Side Postulate (SAS)
• If two sides and the included angle of
one triangle are congruent to two
sides and the included angle of
another, then the triangles are
congruent.
Angle–Side–Angle Postulate (ASA)
• If two angles and the included side of
one triangle are congruent to two
angles and the included side of
another triangle, then the triangles are
congruent.
Angle-Angle-Side (AAS) Postulate:
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

Hypotenuse Leg (HL) Postulate:
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.
Isosceles Triangle Theorem
• If two sides of a triangle are
congruent, then the angles
opposite those sides are
congruent.
Base angles of an
isosceles triangle
are congruent.
• If two angles of a triangle are
congruent, then the sides
opposite those angles are
congruent.
Altitude of a triangle: Segment that starts at
the vertex of a triangle and is perpendicular to
the line containing the opposite side of the
A
triangle.
Altitude from vertex C.
B
C
Altitudes in OBTUSE Triangles:
Altitude from vertex A.
A
B
C
The altitude is
OUTSIDE and
obtuse triangle !
Median
Segment whose endpoints are a
vertex of a triangle and the midpoint of
the opposite side.
How to Draw a Median:
1. Find the midpoint using your ruler.
2. Connect the midpoint to the opposite vertex.
Angle Bisector of a Triangle
A ray that bisects an angle in
a triangle.
45o
45o
Perpendicular Bisector of a Triangle
Segment that passes through the
midpoint of and is perpendicular to the
side of a triangle.
Corollary
Corollary: The bisector of the
vertex angle of an isosceles
triangle is perpendicular to the
base at its midpoint.
Homework
• Pg 628
– 1-12 all
• Pg 629
– 1-14all