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If Two Angles of a Triangle Are Congruent Then the Sides Opposite to Them Are Congruent

The three ang...

Question

The three angles of a triangle are equal to the three corresponding angles of another triangle. Are the triangles necessarily congruent?

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Solution

Given the three angles of a triangle are equal to the three corresponding angles of another triangle
We know that if the three angles of one triangle are equal to three angles of another triangle, then the triangles are similar by the AAA rule and not congruent.
Hence, the triangles will not be 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.

If three angles of a triangle are equal to the corresponding three angles of another triangle then the two triangles are congruent.

Q. Consider the following statements:
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. If all three angles of a triangle are equal to all three angles in another triangle, then the triangles are congruent using AAA congruency.

Q. If three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.

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If Two Angles of a Triangle Are Congruent Then the Sides Opposite to Them Are Congruent

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