The topic congruence occurs in geometry and we say that two figures are said to be congruent triangles if they are same in shape and size, which means that if either object is repositioned, it should coincide precisely to the other figure.
For the students of grade XII here is an example: Here are two triangles which are congruent as their corresponding sides are same in length and Corresponding Angles Definition are same in measure.
If congruence occurs in the above two triangles, then mathematically we can write the relationship as:
∆ ABC ≅ ∆ DEF
The symbol ‘≅’ denotes “is congruent to”.
When we study the properties of congruence, then we realize that the order of the points is important. That means the triangles will coincide if A is placed on D, B on E and C and F.
Whereas, the topic congruence does not go right if we say ∆ ABC ≅ ∆ EFD.
As all the grade XII students can observe that the topic congruence fits in the above example as:
The corresponding sides are equal, i.e., AB = DE, BC = EF and CA = FD and corresponding angles are also equal (∠ A = ∠D , ∠ B = ∠ E, ∠ C = ∠ F ).
One can note that formally, congruence for the set of two points goes like: they are congruent if and only if when one point can be repositioned or transformed into the other point by an isometry, i.e., by rotations, translations and reflections.
To all grade XII students, now we are moving ahead in the topic congruence to the principles of congruent triangles:
1. The SSS principle: As two triangles are equal if all the corresponding sides are equal.
2. The SAS principle: Two triangles are congruent if two pairs of corresponding sides are equal and the angles included between them are also equal.
3. The ASA principle: Two triangles are congruent if two pairs of corresponding angles are same in measure with one pair of equal corresponding sides.
4. The RHS (Right Angle Hypotenuse Side) principle: Two right angled triangles are congruent if the hypotenuses of both the triangles are equal with a pair of equal corresponding sides.
In upcoming posts we will discuss about Properties of quadrilaterals and Mean. Visit our website for information on ICSE syllabus for class 3 maths
For the students of grade XII here is an example: Here are two triangles which are congruent as their corresponding sides are same in length and Corresponding Angles Definition are same in measure.
If congruence occurs in the above two triangles, then mathematically we can write the relationship as:
∆ ABC ≅ ∆ DEF
The symbol ‘≅’ denotes “is congruent to”.
When we study the properties of congruence, then we realize that the order of the points is important. That means the triangles will coincide if A is placed on D, B on E and C and F.
Whereas, the topic congruence does not go right if we say ∆ ABC ≅ ∆ EFD.
As all the grade XII students can observe that the topic congruence fits in the above example as:
The corresponding sides are equal, i.e., AB = DE, BC = EF and CA = FD and corresponding angles are also equal (∠ A = ∠D , ∠ B = ∠ E, ∠ C = ∠ F ).
One can note that formally, congruence for the set of two points goes like: they are congruent if and only if when one point can be repositioned or transformed into the other point by an isometry, i.e., by rotations, translations and reflections.
To all grade XII students, now we are moving ahead in the topic congruence to the principles of congruent triangles:
1. The SSS principle: As two triangles are equal if all the corresponding sides are equal.
2. The SAS principle: Two triangles are congruent if two pairs of corresponding sides are equal and the angles included between them are also equal.
3. The ASA principle: Two triangles are congruent if two pairs of corresponding angles are same in measure with one pair of equal corresponding sides.
4. The RHS (Right Angle Hypotenuse Side) principle: Two right angled triangles are congruent if the hypotenuses of both the triangles are equal with a pair of equal corresponding sides.
In upcoming posts we will discuss about Properties of quadrilaterals and Mean. Visit our website for information on ICSE syllabus for class 3 maths
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