Congruent TrianglesToolkit 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 PartsTJD RCF. List the congruent corresponding parts.

Sides: TJ RC JD CF DT FR Angles: T R J C D F

T

J

D FR

C

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.

a) PQ PS, QR SRb) PR PRc) Q S, QPR

SPRd) QRP SRPee PQR PSR

GivenReflexive PropertyGiven3rd Angles Thm.Definition ofCongruent Triangles

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 CongruencyABC ____

To prove using SSS:

To prove using SAS:

RK TS

RSK TKS

Ex.4: Using SSS or SASRS TK. What other information do you need to prove 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 ProofCan 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?