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If the three sides and three angles of one triangle are equal to the corresponding sides and angles of another triangle, they are known as congruent triangles. In other words, we can say that the corresponding sides and angles of congruent triangles are equal. The triangles can be rotated, flipped turned, or slid to be made to look identical. If the triangles are repositioned, they coincide with each other and can be superimposed on each other. Further, congruence in Mathematics means that two figures are similar to each other. There are four rules of congruency, namely – SSS, SAS, ASA, AAS. We can use any of these to prove the congruence of two triangles. Triangles have six dimensions, i.e., three sides and three angles. If we know 3 out of the six values, the congruence of triangles can be evaluated.

If the length of three sides of one triangle is equal to the corresponding sides of another triangle, then the two triangles are said to be congruent under the SSS rule. If we have a triangle with sides given by AB = 7cm, BC = 3cm and CA = 5cm and another triangle MN = 3cm, NO = 7cm and OM = 5cm. As AB = NO, BC = MN, and CA = OM, the two triangles are congruent.

If two sides of a triangle and the angle between them is equal to the corresponding two sides and angle of another triangle, then the two triangles are congruent under the SAS rule.

If two angles of a triangle and the side included between them are of the same measure as the two angles and the included side of another triangle, then we can say the two triangles are congruent under the ASA rule.

If two angles and any side of a triangle are equal in measure to the corresponding two angles and side of another triangle, then the two triangles are congruent under the AAS rule.

This is another rule that can be applied to right-angled triangles to validate their congruency. The hypotenuse and one side of a right triangle are equal to the corresponding hypotenuse and side of another triangle then they are congruent under the RHS rule.

Congruent triangles are used in the construction to reinforce the structure. This ensures that the structures are strong and rigid. Thus, they do not buckle or bend under strong winds or other weather anomalies.

A truss bridge is formed by equilateral triangles on both sides. All these triangles are congruent under the SSS criteria. This is because the truss bridge needs to have equal weight controlling lengths to keep the structure intact so that it doesn’t fall.

This is common playground equipment. The necessary angles and side lengths must be created so that all the triangles involved are congruent under the ASS rule. One miscalculation in terms of angle, side length, or congruence can be fatal to a child playing on this structure.

To learn more about congruence and other Mathematical topics, enlist the help of the math experts at Cuemath. They use resources such as workbooks, worksheets, math puzzles, games, etc., to teach a class and ensure that a kid masters the subject in no time. Start your journey with Cuemath today and open yourself to a world of opportunities.

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