4.3. Congruent Triangles http://www.ck12.org
Guidance
Recall that two figures are congruent if and only if they have exactly the same size and shape. If two triangles
are congruent, they will have exactly the same three sides and exactly the same three angles. In other words, two
triangles are congruent if you can turn, flip, and/or slide one so it fits exactly on the other.
4 ABCand 4 DEFare congruent because
AB∼=DE^6 A∼=^6 D
BC∼=EF and^6 B∼=^6 E
AC∼=DF^6 C∼=^6 FNotice that when two triangles are congruent their three pairs of corresponding angles and their three pairs of
corresponding sides are congruent.
When referring to corresponding congruent parts of congruent triangles, you can use the phrase Corresponding Parts
of Congruent Triangles are Congruent, or its abbreviation CPCTC.
Properties of Congruence Review
Recall the Properties of Congruence:
Reflexive Property of Congruence:Any shape is congruent to itself.
AB∼=ABor 4 ABC∼= 4 ABC
Symmetric Property of Congruence:If two shapes are congruent, the statement can be written with either shape
on either side of the∼=sign.
(^6) EF G∼= (^6) XY Zand (^6) XY Z∼= (^6) EF Gor 4 ABC∼= 4 DEFand 4 DEF∼= 4 ABC
Transitive Property of Congruence:If two shapes are congruent and one of those is congruent to a third, the first
and third shapes are also congruent.
4 ABC∼= 4 DEFand 4 DEF∼= 4 GHI, then 4 ABC∼= 4 GHI
These three properties will be very important when you begin to prove that two triangles are congruent.
Example A
Are the two triangles below congruent?