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Common mistakes made when working on congruent triangles

Though the students enjoy working with congruent triangles, however in many cases they tend to make mistakes. These mistakes could be because of carelessness or because the child did not understand the concept properly. It is always a good idea to be aware about the common mistakes which students usually make so that these can be corrected from the early age. Here are some of the common mistakes which students usually make when working on congruent triangles.

☞ If two triangles are equal in area, they are also congruent

The correct statement is Two triangles may have the same area, however they MAY or MAY NOT be congruent.

Ways to teach the children to minimize this error
• Let us take an example as given below:
Area of the Triangle ABC having the base and the height as 6 cm and 2 cm respectively is 6 cm².
Area of the Triangle PQR having the base and the height as 4 cm and 3 cm respectively is 6 cm².
In the above example, though the area of triangles ABC & PQR are same (6 cm²), however the corresponding sides (base and height) are not equal.
∴ triangle ABC is not congruent to triangle PQR
• ☞ Two equilateral triangles are also congruent triangles

The correct statement is Two equilateral triangles MAY or MAY NOT be congruent triangles.

Ways to teach the children to minimize this error
• Let us take an example as given below:
An equilateral triangle ABC have all the sides as 6 cm.
An equilateral triangle PQR have all the sides as 9 cm.
In the above example, though the triangles ABC & PQR are equilateral, however the corresponding sides are not equal.
∴ triangle ABC is not congruent to triangle PQR
• ☞ If all the pairs of angles of two triangles are equal, the two triangles are congruent

The correct statement is If all the pairs of angles of two triangles are equal, the two triangles MAY or MAY NOT be congruent.

Ways to teach the children to minimize this error
• Let us take an example as given below:
In triangle ABC, the angles A, B, C are 30°, 90°, 60° and the sides of the triangle are 1 cm, 2 cm, √3 cm.
In triangle PQR, the angles P, Q, R are 30°, 90°, 60° and the sides of the triangle are 2 cm, 4 cm, 2√3 cm
In the above example, though all the pairs of angles of two triangles ABC & PQR are equal, however the corresponding sides are not equal.
∴ triangle ABC is not congruent to triangle PQR
• ☞ Two similar triangles are also congruent triangles

The correct statement is Two similar triangles MAY or MAY NOT be congruent.

Ways to teach the children to minimize this error
• Let us take an example as given below:
An equilateral triangle ABC have all the sides as 6 cm.
An equilateral triangle PQR have all the sides as 9 cm.
In the above example, though the triangles ABC & PQR are equilateral and therefore they are similar, however the corresponding sides are not equal.
∴ triangle ABC is not congruent to triangle PQR

• The best way to remove the above confusion and to ensure the children have less chance of committing mistakes is to practice the problems related to the above situations. Click on Congruence of Triangles to practice.

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Given below are other commonly made mistakes in Math:
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