Download Holt Geometry 4-4

4-4 Triangle Congruence: SSS and SAS
Bell Ringer
1. Name the angle formed by AB and AC.
2. Name the three sides of ABC.
3. ∆QRS  ∆LMN. Name all pairs of
congruent corresponding parts.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
In Lesson 4-3, you proved triangles
congruent by showing that all six pairs
of corresponding parts were congruent.
(3 pair of congruent sides and 3 pair of
congruent angles)
Luckily, there are shortcuts to
prove that 2 triangles are
congruent to each other. We
will learn these today.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
For example, you only need to know that
two triangles have three pairs of congruent
corresponding sides. This can be expressed
as the following postulate.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Remember!
Some triangles can share a side, so
you can apply the Reflexive Property to
get a pair of congruent parts.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Explain why ∆ABC  ∆DBC.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
An included angle is an angle formed
by two adjacent sides of a polygon.
B is the included angle between sides
AB and BC.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Another shortcut uses two pairs of
congruent sides and one pair of
congruent INCLUDED angles.
Holt Geometry
4-4 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 Geometry
4-4 Triangle Congruence: SSS and SAS
Example 2: Engineering Application
The diagram shows part of
the support structure for a
tower. Explain why
∆XYZ  ∆VWZ.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Explain why ∆ABC  ∆DBC.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Example 4: Proving Triangles Congruent
Given: BC ║ AD, BC  AD
Prove: ∆ABD  ∆CDB
Statements
Holt Geometry
Reasons
4-4 Triangle Congruence: SSS and SAS
Check It Out! Example 4
Given: QP bisects RQS. QR  QS
Prove: ∆RQP  ∆SQP
Statements
Holt Geometry
Reasons
4-4 Triangle Congruence: SSS and SAS
An included side is the common side
of two consecutive angles in a polygon.
The following postulate uses the idea of
an included side.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Example 2: Applying ASA Congruence
Determine if you can use ASA to prove the
triangles congruent. Explain.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Use AAS to prove the triangles congruent.
Given: JL bisects KLM, K  M
Prove: JKL  JML
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Example 4A: Applying HL Congruence
Determine if you can use the HL Congruence
Theorem to prove the triangles congruent. If
not, tell what else you need to know.
Holt Geometry
4-4 Triangle Congruence: SSS and SAS
Identify the postulate or theorem that proves
the triangles congruent.
Holt Geometry