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Congruency of Line Segments

Which of the ...

Question

Which of the following triangles have all the three sides congruent to each other?

A

Isosceles triangle

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B

Equilateral triangle

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C

Scalene triangle

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D

Acute angle triangle

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Solution

The correct option is B Equilateral triangle
A line segment is said to be congruent to another if they have same length. Equilateral triangle has all the three sides of same length. Hence, all the sides of equilateral triangle are congruent.

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Q. Which of the following statements are true and which of them are false?

(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two figures have equal areas, they are congruent.
(iv) If two triangles are equal in area, they are congruent.
(v) If two sides and one angle of a triangle are equal to the corresponding two sides and angle of another triangle, the triangle are congruent.
(vi) If two angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent.
(vii) If three angles of a triangle are equal to the corresponding angles of another triangle then the triangles are congruent.
(viii) If the hypotenuse and an acute angle of a right triangle are equal to the hypotenuse and the corresponding acute angle of another right triangle then the triangle are congruent.
(ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.
(x) If two triangles are congruent then their corresponding sides and their corresponding angles are congruent.

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i) If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.
ii) If the three angles of a triangle are equal to three angles of another triangle respectively, then the two triangles are congruent.

Q. Which rule states that if all the three sides of one triangle are equivalent to the corresponding three sides of second triangle, the two triangles are congruent ?

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