Warm Up Check homework answers with each other!. Ch. 4.2-3: Congruence and Triangles Students will prove triangles congruent using SSS, SAS, ASA, AAS,

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Proving Triangles Congruent

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Proving Triangles Congruent

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Presentation transcript:

Warm Up Check homework answers with each other!

Ch : Congruence and Triangles Students will prove triangles congruent using SSS, SAS, ASA, AAS, and HL theorems.

Congruence When two figures are congruent they have exactly the same size and the same shape. CongruentNot Congruent

There has to be a correspondence between their angles and sides, such that corresponding angles and corresponding sides are congruent. Corresponding Sides Corresponding Angles A B C D EF

Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. If  A   D and  B   E, then  C   F. A B C D E F

Right Angle Congruence Theorem All right angles are congruent

Properties of Congruent Triangles Reflexive Property of Congruent Triangles Every triangle is congruent to itself. Symmetric Property of Congruent Triangles If  ABC   DEF, then  DEF   ABC. Transitive Property of Congruent Triangles If  ABC   DEF and  DEF   JKL, then  ABC   JKL.

Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

How are they congruent SAS ASA SSS

Given: Prove: A R G D StatementsReasons

Given: G is the midpoint of Prove: F H E G Statements Reasons

Warm Up 1.Find the value of the variable. The diagram is not to scale. 2.Find the measure of each interior and exterior angle. The diagram is not to scale.

Congruent Triangles proving-triangles-congruent-by-sss-sas- asa-and-aasproving-triangles-congruent-by-sss-sas- asa-and-aas

Given: bisects Prove: A E G C

StatementsReasons

Challenge!!! Given: Prove: HG L J K