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Sides EF , FD and DE of a triangle DEF are produce in order prove that angle DFP angle EDQ angle FER=180?
Verified Answer
Sides EF , FD and DE of a triangle DEF are produce in order prove that...
∠DFP = ∠D + ∠E ...(1)
| Exterior Angle Theorem
∠EDQ = ∠E + ∠F ...(2)
| Exterior Angle Theorem
∠FER = ∠F + ∠D ...(3)
| Exterior Angle Theorem
Adding (1), (2) and (3), we get
∠DFP + ∠EDQ + ∠FER = 2(∠D + ∠E + ∠F)
But ∠D + ∠E + ∠F = 180degree
| ∵ The sum of the three angles of a triangle is 180degree
∴ ∠DFP + ∠EDQ + ∠FER = 2(180degree) = 360degree.
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
Sides EF , FD and DE of a triangle DEF are produce in order prove that...
Proof:
Given:
- Sides EF, FD, and DE of triangle DEF are produced in order.
To prove:
- ∠DFP + ∠EDQ + ∠FER = 180°
Proof:
1. Extend side EF to point P beyond F.
2. Extend side FD to point Q beyond D.
3. Extend side DE to point R beyond E.
Statement 1:
- Exterior angle property:
- ∠DFP = ∠D + ∠F
- ∠EDQ = ∠E + ∠D
- ∠FER = ∠F + ∠E
Statement 2:
- Sum of angles in a triangle is 180°:
- ∠D + ∠E + ∠F = 180°
Conclusion:
- Adding all three equations from Statement 1:
- (∠DFP + ∠EDQ + ∠FER) = (∠D + ∠F) + (∠E + ∠D) + (∠F + ∠E)
- = ∠D + ∠E + ∠F
- = 180°
Therefore, ∠DFP + ∠EDQ + ∠FER = 180°.
Given:
- Sides EF, FD, and DE of triangle DEF are produced in order.
To prove:
- ∠DFP + ∠EDQ + ∠FER = 180°
Proof:
1. Extend side EF to point P beyond F.
2. Extend side FD to point Q beyond D.
3. Extend side DE to point R beyond E.
Statement 1:
- Exterior angle property:
- ∠DFP = ∠D + ∠F
- ∠EDQ = ∠E + ∠D
- ∠FER = ∠F + ∠E
Statement 2:
- Sum of angles in a triangle is 180°:
- ∠D + ∠E + ∠F = 180°
Conclusion:
- Adding all three equations from Statement 1:
- (∠DFP + ∠EDQ + ∠FER) = (∠D + ∠F) + (∠E + ∠D) + (∠F + ∠E)
- = ∠D + ∠E + ∠F
- = 180°
Therefore, ∠DFP + ∠EDQ + ∠FER = 180°.
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Sides EF , FD and DE of a triangle DEF are produce in order prove that angle DFP angle EDQ angle FER=180?
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Sides EF , FD and DE of a triangle DEF are produce in order prove that angle DFP angle EDQ angle FER=180? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Sides EF , FD and DE of a triangle DEF are produce in order prove that angle DFP angle EDQ angle FER=180? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sides EF , FD and DE of a triangle DEF are produce in order prove that angle DFP angle EDQ angle FER=180?.
Sides EF , FD and DE of a triangle DEF are produce in order prove that angle DFP angle EDQ angle FER=180? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Sides EF , FD and DE of a triangle DEF are produce in order prove that angle DFP angle EDQ angle FER=180? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sides EF , FD and DE of a triangle DEF are produce in order prove that angle DFP angle EDQ angle FER=180?.
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