State different rules of congruence of triangles
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Congruence is the term used to define an object and its mirror image. Two objects or shapes are said to be congruent if they superimpose on each other. Their shape and dimensions are the same. In the case of geometric figures, line segments with the same length are congruent and angle with the same measure are congruent.
Two triangles are said to be congruent if all their three sides and three angles are equal. But it is necessary to find all six dimensions. Hence, the congruence of triangles can be evaluated by knowing only three values out of six. The meaning of congruent in Maths is when two figures are similar to each other based on their shape and size. Also, learn about Congruent Figures here
CPCT is the term, we come across when we learn about the congruent triangle. Let’s see the condition for triangles to be congruent with proof.
Congruent Triangles
A polygon made of three line segments forming three angles is known as Triangle.
Two triangles are said to be congruent if their sides have the same length and angles have same measure. Thus two triangles can be superimposed side to side and angle to angle.
In the above figure, Δ ABC and Δ PQR are congruent triangles. This means,
Vertices: A and P, B and Q, and C and R are same.
Sides: AB=PQ, QR= BC and AC=PR;
Angles: ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.
Congruent triangles are triangles having corresponding sides and angles to be equal. Congruence is denoted by the symbol ≅. They have the same area and the same perimeter.
CPCT Rules in Maths
The full form of CPCT is Corresponding parts of Congruent triangles. Congruency can be predicted without actually measuring the sides and angles of a triangle. Different rules of congruency are as follows.
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There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.
SSS (side, side, side) SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. ...
SAS (side, angle, side) ...
ASA (angle, side, angle) ...
AAS (angle, angle, side) ...
HL (hypotenuse, leg)
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