If all the corresponding angles of two triangles are same, then the two triangles are necessarily congruent.

True

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False

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Solution

The correct option is B
False

If all the corresponding angles of two triangles are equal, then triangles will have the same shape, but not necessarily the same size and hence may not be congruent. See the figure below. The corresponding angles of both triangles are equal, but still their sizes are not same and hence they are not congruent.

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Similar questions

State, true or false :
(i) Two similar polygons are necessarily congruent.
(ii) Two congruent polygons are necessarily similar.
(iii) All equiangular triangles are similar.
(iv) All isosceles triangles are similar.
(v) Two isosceles-right triangles are similar.
(vi) Two isosceles triangles are similar if an angle of one is congruent to the corresponding angle of the other.
(vii) The diagonals of a trapezium divide each other into proportional segments.

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.

Q. Fill in the blanks using the correct word given in brackets :

(i) All circles are ......... (congruent, similar).
(ii) All squares are ........(similar, congruent).
(iii) All .......... triangles are similar (isosceles, equilateral):
(iv) Two triangles are similar, if their corresponding angles are .......... (proportional, equal)
(v) Two triangles are similar, if their corresponding sides are ........... (proportional, equal)
(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are ...........(equal, proportional).

State true or false: If all the corresponding angles of two triangles are the same, then the two triangles are necessarily congruent.

If all the corresponding angles of two triangles are same, then the two triangles are necessarily congruent.

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