1. Obj. 17 Congruent TrianglesThe student is able to (I can): Identify congruent parts based on a congruencerelationship statement Identify and prove congruent triangles given Three pairs of congruent sides (Side-Side-Side) Two pairs of congruent sides and a pair of congruentincluded angles (Side-Angle-Side) Two angles and a side (Angle-Side-Angle and Angle-Angle-Side) A Hypotenuse and a Leg of a right triangle

2. congruentpolygonsGeometric figures are congruent if they arethe same ssssiiiizzzzeeee and sssshhhhaaaappppeeee. Correspondingangles and corresponding sides are in thesame position in polygons with the samenumber of sides.Two or more polygons whose correspondingangles and sides are congruent. In acongruence statement, the order of thevertices indicates the corresponding parts.Example: Name the corresponding angles ifpolygon SWIM @ polygon ZERO.S @ Z; W @ E; I @ R; M @ O 3. ExampleR PE DACCorrespondingAnglesR @ CE @ PD @ ACorrespondingSidesED @ PARE @ CPRD @ CAThus, RED @ CPA. 4. SSS Side-Side-SideIf three sides of one triangle are congruentto three sides of another triangle, then thetriangles are congruent.TICNUP467 467TIN @ CUP 5. Example Given: , D is the midpoint ofFR @ ER FEProve: FRD @ ERDFRD ESSSSttttaaaatttteeeemmmmeeeennnnttttssss RRRReeeeaaaassssoooonnnnssss1. FR @ ER1. Given2. D is midpt of FE2. Given3. FD @ ED3. Def. of midpoint4. RD @ RD4. Refl. prop. @5. FRD @ ERD 5. SSS 6. SAS Side-Angle-SideIf two sides and the included angle of onetriangle are congruent to two sides and theincluded angle of another triangle, then thetriangles are congruent.LHSUTALHS @ UTA 7. Example Given: , A is the midpoint ofFA @ EA RMProve: FAR @ EAM FRAMESSSSttttaaaatttteeeemmmmeeeennnnttttssss RRRReeeeaaaassssoooonnnnssss1. FA @ EA1. Given2. FAR @ EAM 2. Vertical s3. A is midpt of RM3. Given4. RA @MA4. Def. of midpoint5. FAR @ EAM 5. SAS 8. ASA Angle-Side-AngleIf two angles and the included side of onetriangle are congruent to two angles andthe included side of another triangle, thenthe triangles are congruent.FLYB UGFLY @ BUG 9. AAS angle-angle-sideIf two angles and a nnnnoooonnnn-iiiinnnncccclllluuuuddddeeeedddd side of onetriangle are congruent to two angles and anon-included corresponding side of anothertriangle, then the triangles are congruent.INWYO UDYOU @ DWINThe non-included sides mmmmuuuusssstttt becorresponding in order for the triangles tobe congruent. 10. ASS angle-side-side(we do not cuss in math class)There is no ASS (or SSA) congruencetheorem.(unless the angle is a right angle see nextslide) 11. HL hypotenuse-legIf the hypotenuse and leg of one righttriangle are congruent to the hypotenuseand leg of another right triangle, then thetwo triangles are congruent.JOEMC ADJOE @ DMAC