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Geometry: Congruence


Corresponding Parts of Triangles

Proving Congruence of Triangles

Problem : If triangles JGS and RPC are congruent, to which segment is segment SJ congruent?

Segment SJ is conguent to segment CR.

Problem : If triangles JHF and TLG are congruent, which angle is congruent to angle L?

Angle H

Problem : Why aren't two triangles with three pairs of congruent angles necessarily congruent?

Because angles only determine the relationship between the directions of the segments of a triangle; the lengths of the sides have no limit.

Problem : When the lengths of the sides of two triangles are the same, those triangles are congruent. Using symbols and the correct correspondence, write that the two triangles below are congruent.

There are six ways to properly label the triangles: (1) Triangle CLG is congruent to triangle FDR, (2) LGC is congruent to DRF, (3) GCL and RFD, (4) CGL and FRD, (5) GLC and RDF, and (6) LCG and DFR.

Problem : Is it possible for five parts of a triangle to be congruent to five corresponding parts of another triangle, and the triangles aren't congruent?

No. This would mean that either 3 sides and 2 angles are congruent and the third pair of angles isn't congruent (this is impossible by the triangle angle sum), or 3 angles and 2 sides are congruent, and the third side isn't congruent (this is impossible also, because when 3 angles and even just one side are fixed, the triangle is determined).