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A campen is that by volunteers of mathematical club to boost school and its surrounding under swachh Bharat abhiyan they made their own logo for their campaign. if it is given that triangle ABC is congruent to triangle ECD, BC is equal to ae
prove that angle abc is congruent to angles CEA?
prove that angle abc is congruent to angles CEA?
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A campen is that by volunteers of mathematical club to boost school an...
To prove that ∠ABC ≅ ∠CEA under the given conditions, we can utilize the properties of congruent triangles.
Given Information
- Triangle ABC is congruent to triangle ECD (ΔABC ≅ ΔECD).
- BC = AE.
Congruent Triangles
- Since ΔABC ≅ ΔECD, all corresponding angles and sides are equal:
- ∠A ≅ ∠E
- ∠B ≅ ∠C
- ∠C ≅ ∠D
- AB = EC
- AC = ED
- BC = AE (given).
Corresponding Angles
- From the congruence of the triangles, we have:
- ∠ABC = ∠C and ∠CED = ∠A.
Applying the Given Condition
- We know BC = AE, which means the side opposite to angle ∠ABC in triangle ABC is equal to the side opposite to angle ∠CEA in triangle ECD.
Using Properties of Congruence
- Since triangles ABC and ECD are congruent:
- If BC = AE, we can establish the relationship of the angles based on the congruence.
Conclusion
- Therefore, by the properties of congruent triangles, we conclude:
- ∠ABC ≅ ∠CEA.
This concludes that not only are the triangles congruent, but the angles corresponding to the equal sides also demonstrate congruence. Thus, the proof is established.
Given Information
- Triangle ABC is congruent to triangle ECD (ΔABC ≅ ΔECD).
- BC = AE.
Congruent Triangles
- Since ΔABC ≅ ΔECD, all corresponding angles and sides are equal:
- ∠A ≅ ∠E
- ∠B ≅ ∠C
- ∠C ≅ ∠D
- AB = EC
- AC = ED
- BC = AE (given).
Corresponding Angles
- From the congruence of the triangles, we have:
- ∠ABC = ∠C and ∠CED = ∠A.
Applying the Given Condition
- We know BC = AE, which means the side opposite to angle ∠ABC in triangle ABC is equal to the side opposite to angle ∠CEA in triangle ECD.
Using Properties of Congruence
- Since triangles ABC and ECD are congruent:
- If BC = AE, we can establish the relationship of the angles based on the congruence.
Conclusion
- Therefore, by the properties of congruent triangles, we conclude:
- ∠ABC ≅ ∠CEA.
This concludes that not only are the triangles congruent, but the angles corresponding to the equal sides also demonstrate congruence. Thus, the proof is established.
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A campen is that by volunteers of mathematical club to boost school and its surrounding under swachh Bharat abhiyan they made their own logo for their campaign. if it is given that triangle ABC is congruent to triangle ECD, BC is equal to ae prove that angle abc is congruent to angles CEA?
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A campen is that by volunteers of mathematical club to boost school and its surrounding under swachh Bharat abhiyan they made their own logo for their campaign. if it is given that triangle ABC is congruent to triangle ECD, BC is equal to ae prove that angle abc is congruent to angles CEA? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A campen is that by volunteers of mathematical club to boost school and its surrounding under swachh Bharat abhiyan they made their own logo for their campaign. if it is given that triangle ABC is congruent to triangle ECD, BC is equal to ae prove that angle abc is congruent to angles CEA? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A campen is that by volunteers of mathematical club to boost school and its surrounding under swachh Bharat abhiyan they made their own logo for their campaign. if it is given that triangle ABC is congruent to triangle ECD, BC is equal to ae prove that angle abc is congruent to angles CEA?.
A campen is that by volunteers of mathematical club to boost school and its surrounding under swachh Bharat abhiyan they made their own logo for their campaign. if it is given that triangle ABC is congruent to triangle ECD, BC is equal to ae prove that angle abc is congruent to angles CEA? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A campen is that by volunteers of mathematical club to boost school and its surrounding under swachh Bharat abhiyan they made their own logo for their campaign. if it is given that triangle ABC is congruent to triangle ECD, BC is equal to ae prove that angle abc is congruent to angles CEA? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A campen is that by volunteers of mathematical club to boost school and its surrounding under swachh Bharat abhiyan they made their own logo for their campaign. if it is given that triangle ABC is congruent to triangle ECD, BC is equal to ae prove that angle abc is congruent to angles CEA?.
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