In two triangles ABC and DEF, it is given that ∠A = ∠D, ∠B = ∠E and ∠C = ∠F. Are the two triangles necessarily congruent?
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No There are only 4 rules when we can say two triangles are congurent=ASA rule,SSS rule,SAS rule, RHS Rule
There is not AAA rule for congurenve So ABC and DBC are not congurent in given Conditions
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Answered by
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The triangles ΔABC and ΔDEF are not congruent to each other but they are similar triangle.
Step-by-step explanation:
- Condition congruence of two triangle are given below
- By SSS rules . Means if two triangle have all three corresponding side are equal , they must be congruent to each other.
- By SAS rules. Means if two triangle have two corresponding side and angle between corresponding side are equal , they must be congruent to each other.
- By ASA rules. Means if two triangle have two corresponding angle and side between corresponding angle are equal , they must be congruent to each other.
- By AAS rules. Means if two triangle have two corresponding adjacent angle and next side are equal , they must be congruent to each other.
- By RHS rules. Means if two triangle are right angle triangle, corresponding hypotenuse and one other side are equal,they must be congruent to each other.
- Now come to question, here it is given that
∠A = ∠D, ∠B = ∠E and ∠C = ∠F
- It is not satisfied above five condition of congruence of two triangle.
So triangles ΔABC and ΔDEF are not congruent to each other.
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