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Assertion (A) : If two triangles are con...

Assertion (A) : If two triangles are congruent their corresponding angles are equal.
Reason (R ) : Area of two congruent triangles are equal.

A

Both A and R are correct and Statement R is true explanation of Statement A

B

Both A and R are correct but Statement R is not a true explanation of Statement A

C

Statement A is correct, Statement R is wrong

D

Statement A is wrong, Statement R is correct

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given question, we need to analyze the Assertion (A) and Reason (R) provided. ### Step-by-Step Solution: 1. **Understanding Assertion (A)**: - The assertion states that if two triangles are congruent, their corresponding angles are equal. - This is a fundamental property of congruent triangles. By definition, congruent triangles are identical in shape and size, which means all corresponding angles and sides are equal. 2. **Understanding Reason (R)**: - The reason states that the area of two congruent triangles is equal. - While it is true that congruent triangles have equal areas, the area alone is not a criterion for congruence. Two triangles can have the same area but different shapes, which means they are not necessarily congruent. 3. **Evaluating the Statements**: - Since Assertion (A) is true (congruent triangles have equal corresponding angles), we can agree with this part. - However, Reason (R) is misleading because it implies that area can be used to determine congruence, which is incorrect. Therefore, while the area of congruent triangles is equal, it does not serve as a basis for establishing congruence. 4. **Conclusion**: - Assertion (A) is true, but Reason (R) is false. Thus, the correct relationship between the two statements is that the assertion is correct, while the reason is incorrect. ### Final Answer: - Assertion (A) is true. - Reason (R) is false.
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Knowledge Check

  • All the congruent triangles have _______ area.

    A
    Unequal
    B
    one third
    C
    equal
    D
    none of these
  • Assertion : If we draw two triangles with angles 30^(@), 70^(@) and 80^(@) and the length of the sides of one triangle be different than that of the corresponding sides of the other triangle then two triangles are not congruent. Reason : If two triangles are constructed which have all corresponding angles equal but have unequal corresponding sides, then two triangles cannot be congruent to each other.

    A
    If both assertion and reason are true and reason is the correct explanation of assertion.
    B
    If both assertion and reason are true but reason is not the correct explanation of assertion.
    C
    If assertion is true but reason is false.
    D
    If assertion is false but reason is true.
  • Assertion (A): Two similar triangles are always congruent. Reason (R ): It the area of two similar triangles are equal then the triangles are congruent

    A
    Both A and R are true R is the correct explanation for A.
    B
    Both A and R are true nad R is not correct explanation for A.
    C
    A is true but R is false.
    D
    A is false but R is true.
  • Similar Questions

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    Two triangles are congruent if three angles of one triangle are equal to three angles of the other triangle.

    Prove that for a given correspondence, if three angles of one triangles are congruent to the corresponding three angles of the other triangle, then the two triangles are similar.

    If two triangles have their corresponding angles equal, are they always congruent? If not, draw two triangles which are not congruent but which have their corresponding angles equal