Congruent Triangles

       
           

By the term Congruence Of Triangles, we mean that two given Triangles are Congruent Triangles. When measure of corresponding sides and the corresponding angles are equal then triangles are congruent. Thus we say that the Triangle Congruence means that if two triangles are placed one over another, then we say that the two figures overlap each other. Thus we say that the two triangles are congruent, we say that the triangles are congruent, then the corresponding line segments are of equal measure. Now we look at the different properties which satisfy the congruency of the triangles. There are four different properties of congruency of the triangles. Let us take them one by one:

1.      ASA (Angle Side Angle) property: If two corresponding angles of triangles and the enclosed side of two triangles are equal, then we say that two given triangles are congruent. By the word enclosed side, we say that the sides which exist between the two equal angles of the two different triangles are equal.

2.      SAS (Side Angle Side) Property: By SAS Property, we mean that if we have two triangles, then the two corresponding sides of the two triangles and the enclosed angle of the two triangles are equal then two given triangles are congruent.

3.      SSS (Side Side Side) Property: By SSS Property, we mean that  if we have two triangles, such that all the corresponding sides of one triangle is equal to the side of the another triangle, then we say that two triangles are congruent by the SSS Property of congruency of the two triangles .

4.       RHS (Right Hypotenuse Side) Property: By RHS Property, we mean that the two triangles are congruent, if we say that the two angles are right angled of the right triangles, and the hypotenuse of two triangles are equal and one pair of corresponding sides of two triangles are equal, then we say that by the property of RHS, the two triangles are congruent.

We can use above mentioned properties for proving two triangles similar and these similar triangles are in turn congruent to each other. It should be noted that we need at least two triangles to be congruent

       
In the figure, ∆ABC ≅ ∆DEF.
a) When ∆ABC ≅ ∆DEF, then sides of ∆DEF fall on corresponding equal sides of
∆ABC, i.e., DE covers AB or DE ↔ AB; EF covers BC or EF ↔ BC and FD
covers CA or FD ↔ CA.
b) In case ∆ABC ≅ ∆DEF,
angle D covers angle A or angle D ↔ angle A.
angle E covers angle B or angle E ↔ angle B.
angle F covers angle C or angle F ↔ angle C.
c) In case ∆ABC ≅ ∆DEF
D corresponds to A or D ↔ A.
E corresponds to B or E ↔ B.
F corresponds to C or F ↔ C.
d) In congruent triangles, corresponding parts are equal and we write in short
‘c.p.c.t.’ “for Corresponding Parts of Congruent Triangles”.

Topics Covered in Congruent Triangles

criteria for congruence of triangles

a) SAS Criteria:
If two Triangles are such that two sides and the included angle of the one equal to
the
corresponding sides and the included angle of the other, then the Triangles are
congruent.
In ...Read More

Math Topics