Congruent Triangles in Grade XI

Hello Friends, in today's session we all are going to discuss one of Geometry topic. Geometry is one of the most interesting topics of mathematics that is Finding the Area of a Triangle. Today we will discuss triangles more specifically congruence triangle . A grade XI student is aware of the term Geometry. So we don’t need to discuss it. We will quickly move on to our topic.

What is congruence triangle? The term congruence defines the fact that when one object completely coincides with other. That is they are the mirror image of one another. When we put one object on to the other one it completely hides the other one.
In case of triangles, triangles are called congruent triangle when their corresponding sides and interior angles are congruent.
Triangles have three main magnitudes:

1.      Sides

2.      Angles

3.      Area

To prove two triangles are congruent we have to prove:

1.      They have equal corresponding sides.

2.      They have equal corresponding angles.

3.      Their areas are equal.

But we don’t have to prove all of them. We just group some of these. That is certain group of ( Sides, Angles and Area) will do that:

1.      SSS - We have 5 ways to prove two triangles are congruent. SSS that is Side – Side – Side. If all the three sides of a triangle are equal to corresponding 3 sides of other triangle then the triangles are congruent. As we will now prove that two triangles are congruent then their angles are also equal. That is angle P = L, Q = M and R = M 

2.      SAS: Side- Angle- Side. When two corresponding sides and their included angle of one triangle are equal to the other triangle then the two triangles are called congruent triangle. Now if triangles are equal then their remaining sides and angles are also equal. As we will now prove that two triangles are congruent then their third side PQ = LM and two remaining angle, angle P = L and Q = M.

         

3.      ASA:  Angle- Side- Angle. When two angles and their included sides are equal to the other triangle then the two triangles are called congruent. Similarly when triangles are proved congruent then the remaining angles R and N and the two sides are also equal  PR = LN and QR = MN

4.      AAS: Angle- Angle- Side. If two pairs of corresponding angles and a pair of corresponding opposite side of two triangles are equal then both the triangles are congruent. Hence other two side PQ = LM and PR = LN and also angle Q = M.

5.      RHS: Right- Angle- Hypotenuse- Side. When two right-angled triangles have their hypotenuses equal in length and the shorter sides of two right triangles is equal in length, the triangles are called as congruent triangle. Now when triangles are proved congruent then the remaining third side PQ = LM and two angles Q = M and R = N are also equal

           

Now we have discussed congruent triangles and triangle congruence principles. We had also discussed facts which prove two triangles are congruent or not.

In upcoming posts we will discuss about Basic Constructions in Grade XI and reflections. Visit our website for information on CBSE syllabus 12th