Download Are the Triangles Congruent?

Congruent Triangles
Toolkit 4.1-4.3
Today’s Goals:
To recognize congruent figures.
To prove two triangles congruent.
Congruent Polygons


If two polygons are congruent, then all the
angles are congruent
And all the sides are congruent.
Ex.1: Naming Congruent Parts
TJD  RCF. List the congruent corresponding parts.


Sides: TJ  RC
Angles: T R
JD  CF
DT  FR
J C
D F
D
F
R
J
C
T
Third Angles Theorem

If two angles of one triangle are congruent to two
angles of another triangle, then the third angles
are congruent.
CF
Ex. 2: Finding Congruent Triangles
Ex.3: Proving Triangles Congruent
Use the information given in the diagram.
Give a reason why each statement is true.
Given
PQ  PS, QR  SR
Reflexive Property
b) PR  PR
Given
c) Q S, QPR SPR
3rd Angles Thm.
d) QRP SRP
Definition of
e) PQR  PSR
Congruent Triangles
a)
Shortcuts to Proving Two
Triangles Congruent


Enrichment Activity
Work with your partners…
Side-Side-Side (SSS)

If the three sides of one triangle are congruent
to the three sides of another triangle, then the
two triangles are congruent.
Use SSS to Prove Congruency
ABC   ______
Included Angle

The angle between two sides (segments).

B is included between AB and CB.
B
A
C
Side-Angle-Side (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 two triangles are congruent.
ABC  ____
Use SAS to Prove Congruency
ABC  ____
Ex.4: Using SSS or SAS
RS  TK. What other information do you need to prove
RSK  TKS?

To prove using SSS:
RK  TS

To prove using SAS:
RSK  TKS
Ex.5: Are the Triangles Congruent?
From the information given, can you prove
RED  CAT ?
No, not enough information to prove RED  CAT.
T is not included between CA and CT.
Ex. 6:
From the given information, can you
prove that AEB  DBC? Explain.

Given: EB  CB
AE  DB
Two-Column Proof
Can you use SSS or SAS to prove congruency?


Given: FG || KL, FG  KL
Prove: FGK  KLF
Angle-Side-Angle (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 two
triangles are congruent.
ABC  XZY
ASA
ABC  CDA
Angle-Angle-Side (AAS)

If two angles and a nonincluded side of one triangle are congruent
to two angles and the corresponding nonincluded side of another
triangle, then the triangles are congruent.
ABC  YXZ
AAS
ABC  DEC
SUMMARY:
Determine if you can prove the triangles
congruent. Which method would you use?