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In the given figure angle CEF=angle CFE. F is the mid-point of DC. Prove that AB/BD=AE/FD.?
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In the given figure angle CEF=angle CFE. F is the mid-point of DC. Pro...
Given Information
- Angle CEF = Angle CFE
- F is the midpoint of DC
Objective
Prove that AB/BD = AE/FD.
Proof Strategy
To prove the relationship, we will use properties of similar triangles and the concept of midpoints.
Step 1: Analyzing the Triangles
- Triangles CEF and CFE are isosceles since angles CEF and CFE are equal.
- Since F is the midpoint of DC, we have DF = FC.
Step 2: Establishing Similarity
- From the angle property, triangles AEF and ABD can be established as similar due to Angle-Angle (AA) similarity criterion:
- Angle AEF = Angle ABD (common angle)
- Angle CEF = Angle CFE (given)
Step 3: Using the Proportionality of Similar Triangles
- From the similarity of triangles AEF and ABD, we can set up the ratio:
- AB/BD = AE/EF
Step 4: Relating EF to FD
- Since F is the midpoint of DC:
- EF = FD as both segments are equal.
Conclusion
- By substituting EF with FD in the similarity ratio, we have:
- AB/BD = AE/FD
Thus, we have proved that AB/BD = AE/FD, completing the proof.
- Angle CEF = Angle CFE
- F is the midpoint of DC
Objective
Prove that AB/BD = AE/FD.
Proof Strategy
To prove the relationship, we will use properties of similar triangles and the concept of midpoints.
Step 1: Analyzing the Triangles
- Triangles CEF and CFE are isosceles since angles CEF and CFE are equal.
- Since F is the midpoint of DC, we have DF = FC.
Step 2: Establishing Similarity
- From the angle property, triangles AEF and ABD can be established as similar due to Angle-Angle (AA) similarity criterion:
- Angle AEF = Angle ABD (common angle)
- Angle CEF = Angle CFE (given)
Step 3: Using the Proportionality of Similar Triangles
- From the similarity of triangles AEF and ABD, we can set up the ratio:
- AB/BD = AE/EF
Step 4: Relating EF to FD
- Since F is the midpoint of DC:
- EF = FD as both segments are equal.
Conclusion
- By substituting EF with FD in the similarity ratio, we have:
- AB/BD = AE/FD
Thus, we have proved that AB/BD = AE/FD, completing the proof.
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In the given figure angle CEF=angle CFE. F is the mid-point of DC. Prove that AB/BD=AE/FD.?
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In the given figure angle CEF=angle CFE. F is the mid-point of DC. Prove that AB/BD=AE/FD.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In the given figure angle CEF=angle CFE. F is the mid-point of DC. Prove that AB/BD=AE/FD.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure angle CEF=angle CFE. F is the mid-point of DC. Prove that AB/BD=AE/FD.?.
In the given figure angle CEF=angle CFE. F is the mid-point of DC. Prove that AB/BD=AE/FD.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In the given figure angle CEF=angle CFE. F is the mid-point of DC. Prove that AB/BD=AE/FD.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure angle CEF=angle CFE. F is the mid-point of DC. Prove that AB/BD=AE/FD.?.
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