Review on Triangle Congruency

Shortcuts in Triangle Congruency We learned that two polygons were congruent if EACH corresponding pair of angles were congruent AND each pair of corresponding sides were congruent. Remember that you had to LIST EACH PAIR? Yikes! That could get very long and tedious (tiring).

That’s why… ,[object Object],[object Object],[object Object]

Side Side Side ,[object Object],A B C 3 inches 7 inches 5 inches X P N 3 inches 7 inches 5 inches AC PX AB PN CB XN Therefore, using SSS, ∆ ABC = ∆PNX ~ = ~ = ~ = ~

Side Angle Side ,[object Object],A B C 3 inches 5 inches 60 ° X P N 3 inches 5 inches 60 ° CA XP CB XN  C  X Therefore, by SAS, ∆ ABC ∆PNX = ~ = ~ = ~ = ~

Angle Side Angle ,[object Object],A B C 3 inches 60 ° 70 ° X P N 3 inches 60 ° 70 ° CA XP  A  P  C  X Therefore, by ASA, ∆ ABC ∆PNX = ~ = ~ = ~ = ~

Side Angle Angle ,[object Object],5 m 60° 70° 5 m These two triangles are congruent by SAA 60 ° 70 °

Remembering our shortcuts ,[object Object],[object Object],[object Object],[object Object],[object Object]

Corresponding parts ,[object Object],[object Object],[object Object],A C B G E F That means that EG  CB What is AC congruent to? FE

Corresponding parts of congruent triangles are congruent. Corresponding parts of congruent triangles are congruent. Corresponding parts of congruent triangles are congruent. Corresponding parts of congruent triangles are congruent.

[object Object],C orresponding P arts of C ongruent T riangles are C ongruent. You can only use CPCTC in a proof AFTER you have proved congruence. CPCTC

For example: ,[object Object],A F E D C B Statements Reasons AC  DF Given  C   F Given CB  FE Given Δ ABC  Δ DEF SAS AB  DE CPCTC

Review on Triangle Congruency

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Review on Triangle Congruency