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As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once
there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the
help of a rope which normal board electricians were carrying on bicycles.
This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o
with line AC. show that ∆APC and ∆BPC are congruent?
there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the
help of a rope which normal board electricians were carrying on bicycles.
This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o
with line AC. show that ∆APC and ∆BPC are congruent?
Most Upvoted Answer
As shown In the village of Surya there was a big pole PC. This pole wa...
Understanding the Problem
In the village of Surya, we have a pole PC, a wire of 10 m length, and a staircase reaching point P on the pole, forming a 60° angle with line AC. We need to show that triangles ∆APC and ∆BPC are congruent.
Identifying the Triangles
- Let A be the base of the pole on the ground.
- Let B be a point on line AC such that AB = AC, establishing ∆APC and ∆BPC.
- Both triangles share the side PC (the pole).
Using Congruence Criteria
To prove the triangles are congruent, we can use the following criteria:
1. **Side-Side-Side (SSS)**:
- In both triangles, we have:
- PC (common side) = PC
- AP = BP (since the angle at P is 60°, hence both lengths are equal due to symmetry)
2. **Angle**:
- The angle ∠APC = ∠BPC = 60° (given).
Conclusion of Congruence
- Since both triangles share side PC, have equal lengths (AP = BP), and have equal angles (∠APC = ∠BPC), we can conclude:
∆APC ≅ ∆BPC
This establishes that triangles ∆APC and ∆BPC are congruent by the SSS congruence criterion. Thus, the electricians can confidently use the staircase to reach point P on the pole, ensuring they are working on a stable and structurally sound arrangement.
This geometric analysis demonstrates the importance of congruence in practical applications, such as repairs in the village of Surya.
In the village of Surya, we have a pole PC, a wire of 10 m length, and a staircase reaching point P on the pole, forming a 60° angle with line AC. We need to show that triangles ∆APC and ∆BPC are congruent.
Identifying the Triangles
- Let A be the base of the pole on the ground.
- Let B be a point on line AC such that AB = AC, establishing ∆APC and ∆BPC.
- Both triangles share the side PC (the pole).
Using Congruence Criteria
To prove the triangles are congruent, we can use the following criteria:
1. **Side-Side-Side (SSS)**:
- In both triangles, we have:
- PC (common side) = PC
- AP = BP (since the angle at P is 60°, hence both lengths are equal due to symmetry)
2. **Angle**:
- The angle ∠APC = ∠BPC = 60° (given).
Conclusion of Congruence
- Since both triangles share side PC, have equal lengths (AP = BP), and have equal angles (∠APC = ∠BPC), we can conclude:
∆APC ≅ ∆BPC
This establishes that triangles ∆APC and ∆BPC are congruent by the SSS congruence criterion. Thus, the electricians can confidently use the staircase to reach point P on the pole, ensuring they are working on a stable and structurally sound arrangement.
This geometric analysis demonstrates the importance of congruence in practical applications, such as repairs in the village of Surya.
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As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. show that ∆APC and ∆BPC are congruent?
Question Description
As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. show that ∆APC and ∆BPC are congruent? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. show that ∆APC and ∆BPC are congruent? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. show that ∆APC and ∆BPC are congruent?.
As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. show that ∆APC and ∆BPC are congruent? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. show that ∆APC and ∆BPC are congruent? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. show that ∆APC and ∆BPC are congruent?.
Solutions for As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length. Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually repaired with the help of a rope which normal board electricians were carrying on bicycles. This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make 60o with line AC. show that ∆APC and ∆BPC are congruent? in English & in Hindi are available as part of our courses for UPSC.
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