4.3. Congruent Triangles http://www.ck12.org
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?
To determine if the triangles are congruent, each pair of corresponding sides and angles must be congruent.
Start with the sides and match up sides with the same number of tic marks. Using the tic marks:BC∼=MN,AB∼=
LM,AC∼=LN.
Next match the angles with the same markings;^6 A∼=^6 L,^6 B∼=^6 M, and^6 C∼=^6 N. Because all six parts are
congruent, the two triangles are congruent.
Example B
In order to say that 4 ABD∼= 4 ABC, you must determine that the three corresponding angles and sides are congruent.
Which pair of sides is congruent by the Reflexive Property?
The sideABis shared by both triangles. So, in a geometric proof,AB∼=ABby the Reflexive Property of Congruence.
Example C
If all three pairs of angles for two given triangles are congruent does that mean that the triangles are congruent?
Without knowing anything about the lengths of the sides you cannot tell whether or not two triangles are congruent.
The two triangles described above might
Watch this video for help with the Examples above.
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