Question

If all three ____________ of a triangle are respectively equal to that of other triangle, the triangle may not be congruent.

Answer 1

❒ Your Answer:

☁️ If all three angles of a triangle are respectively equal to that of the of other triangle, the triangle may not be congruent.

❒ Reason:

☁️ The triangles may be similar but not congruent. Because, all angles doesn't mean that all sides are also equal, they might have different shapes. For understanding this statement, Here is an example:

⦿ Examples:

• All angles of a equilateral triangle are equal. That is 60°-60°-60° but not all equilateral triangles are equal in size. There is triangle with all angles 60° and another triangle with angles 60°, But their sides are 5 cm, and 2cm respectively. This proves that , they aren't congruent.

So, It is not necessary that corresponding angles are equal, then there corresponding sides are also equal. Hence, they are not always congruent$.$

❒ Explore more!

☁️ Two triangles are congruent, if they coincides with each other. The corresponding vertices, corresponding sides and corresponding angles are equal. Critetions:

• SAS (Side-Angle-Side)

Two triangles are congruent, if two sides and included angle is equal to corresponding sides and included angle.

• ASA (Angle-Side-Angle)

Two triangles are congruent, if two angles and included side of one triangle is equal to corresponding angles and included sides.

• AAS (Angle-Angle-Side)

Two triangles are congruent, if any two pair of angles and a side is equal to corresponding pair of angles and side.

• SSS (Side-Side-Side)

Two triangles are congruent, if all the sides are equal to the corresponding sides of other triangle.

• RHS (Right angle-Hypotenuse-side)

Two right angled triangles are congruent, if the hypotenuse and one side of the triangle is equal to the corresponding hypotenuse and side.

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Answer 2

Answer:

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If all three angles of a triangle are respectively equal to that of other triangle, the triangle may not be congruent