Download Holt McDougal Geometry 4-5

4-5 Triangle Congruence: SSS and SAS
Objectives
Apply SSS and SAS to construct
triangles and solve problems.
Prove triangles congruent by using SSS
and SAS.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Vocabulary
triangle rigidity
included angle
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
You only need to know that two triangles have
three pairs of congruent corresponding sides to
say that the triangles are congruent. This can
be expressed as the following postulate.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Remember!
Adjacent triangles share a side, so you
can apply the Reflexive Property to get
a pair of congruent parts.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Example 1A: Using SSS to Prove Triangle Congruence
Use SSS to explain why ∆ABC  ∆DBC.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Check It Out! Example 1B
Use SSS to explain why
∆ABC  ∆CDA.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
An _____________is an angle formed by
two adjacent sides of a polygon.
is the included angle between sides AB
and BC.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
It can also be shown that only two
pairs of congruent corresponding sides
are needed to prove the congruence of
two triangles if the included angles are
also congruent.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Caution
The letters SAS are written in that order
because the congruent angles must be
between pairs of congruent corresponding
sides.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Example 2A: Engineering Application
The diagram shows part of
the support structure for a
tower. Use SAS to explain
why ∆XYZ  ∆VWZ.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Check It Out! Example 2B
Use SAS to explain why
∆ABC  ∆DBC.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
The SAS Postulate guarantees that
if you are given the lengths of two
sides and the measure of the
included angles, you can construct
one and only one triangle.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Example 3A: Verifying Triangle Congruence
Show that the triangles are congruent for the
given value of the variable.
∆MNO  ∆PQR, when x = 5.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Example 3B: Verifying Triangle Congruence
Show that the triangles are congruent for the
given value of the variable.
∆STU  ∆VWX, when y = 4.
Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Example 4A: Proving Triangles Congruent
Given: BC ║ AD, BC  AD
Prove: ∆ABD  ∆CDB
Statements
Reasons
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2.
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Holt McDougal Geometry
4-5 Triangle Congruence: SSS and SAS
Check It Out! Example 4B
Given: QP bisects RQS. QR  QS
Prove: ∆RQP  ∆SQP
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
Holt McDougal Geometry