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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. F. R. D. C. J. T. - PowerPoint PPT Presentation
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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?