Download SSS and SAS Congruence Notes

Geometry
Triangle Congruence by SSS and SAS
Notes
Date: _____
Objective: To prove two triangles congruent using the SSS and SAS Postulates
In section 4-1 you learned that if two triangles have three pairs of congruent corresponding angles
and three pairs of congruent corresponding sides, then the triangles are congruent.
If you know this:
A  X
B  Y
AB  XY
C  Z
BC  YZ
AC  XZ
Then you know this: ________  ________
However, you do not need to know that all _____ corresponding parts are ______________ in order
to conclude that two triangles are _____________. We have 5 ‘shortcuts’ that we will learn the rest
of this unit that can help us prove that 2 triangles are congruent. This section introduces the first 2
shortcuts.
Side-Side-Side Postulate (SSS)
If three sides of one triangle are congruent to
the three sides of another triangle, then
Example 1: The bridge girders are the same size, as marked. Explain why ABD  CBD.
Example 2:
Example 3: The triangles below are congruent by SSS. Write a congruence statement.
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
triangle, then
*The word _________________ is used frequently when referring to the angles and sides of a
triangle.
Draw BNX below.
BX is included between ____ and ______.
N is included between ____ and ______.
Example 4: The triangles below are congruent by SAS. Write a congruence statement.
Example 5:
Given: P is the midpoint of AE and BK .
Prove: ABP  EKP .
(The “trick” to these kind of triangle proofs
is you will always have enough information
to get 3 congruent parts to use a shortcut.)
Statements
P is the midpoint of AE
Justifications
Definition of midpoint
P is the midpoint of BK
ABP  EKP
Example 6: RS  TK . What other information do you need to prove RSK  TKS by SAS?
Example 7: What other information do you need to prove ABC  CDA by SAS?
Example 8: From the information given, can you prove the two triangles congruent?
If so, state the postulate that proves them congruent.
If not, explain why.
A) RED  CAT
B) AEB  DBC
C) D is the midpoint of AB .