Congruent Triangles Definition
Congruent Triangles Definition
Introduction:- We examine two triangles which are congruent because all
corresponding angles and sides have the same measures. We discuss
circumstances which guarantee that two triangles are congruent.
Definition:- Two triangles are said to be congruent if the corresponding angles
and sides have the same measurements. This means that there are six
corresponding parts with the same measurements.
Under certain circumstances, it is only necessary to know that three
corresponding parts have the same measures in order to guarantee that two
triangles are congruent. We summarize these situations below without proof.
<-- SSS - Two triangles are congruent if all three sides have equal measures.
<-- SAS - Two triangles are congruent if two sides and the included angle have
the same measures.
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<-- ASA - Two triangles are congruent if two angles and the side between them
have the same measures.
<-- AAS - Two triangles are congruent if two angles and a third side have the
same measure.
<-- HL - Two right triangles are congruent if their hypotenuses and one leg have
the same measure.
<-- HA - Two triangles are congruent if their hypotenuses and one of the acute
angles have the same measure.
As soon as the above facts are established, we know that the two triangles are
congruent and also that all six of their corresponding angles and sides have the
same measures.
When two triangles such as ABC and XYZ are congruent and angles correspond as
follows: AX, BY, and CZ we write this congruence as . We illustrate some of
these situations below.
To understand we assume that we have two triangles ABC and A'B'C' in which
ABC contains three sides a, b, c respectively and triangle A'B'C' contains three
sides a', b' and c' respectively.
So according to first condition if two pairs of sides of both triangles and one angle
of both triangles is same then we can say that triangles are congruent. So we can
write that
b = b', c = c' and <A = <A then triangles ABC and A'B'C' are congruent.
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If in case that if two triangles ABC and A'B'C' have two pair of angles are same
with one side is common in both then the triangles are said to be congruent.
<A = <A', <B = <B' and c = c' then triangles ABC and A'B'C' are congruent.
If all sides of triangle ABC and triangle A'B'C' are same then we can say that
triangles are congruent. So we can write that a=a', b=b', c= c',
To understand congruence triangles more deeply we take an example where we
have two triangles DEF and D'E'F'. Now we have to find that both triangles are
Geometry congruent triangles or not.
The sides of DEF are d = 1 , e = 2 and f= 3. The triangle D'E'F' sides are d' =
1, e'= 2 and f'=3. Now we have to find out that both triangles are congruent or
not.
Here we can easily see that sides of both triangles are same so
d = d' = 1, e = e'= 2, f= f'=3
Both triangles are congruent triangle.


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