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20 Read the following text carefully and answer the questions that follow:
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 thatit can reach at point P on the pole and this should make 60° with line AC.
9. Show thatΔ APC and Δ BPC are congruent. (1)
10. Find the value of∠ x. (1)
11. What is the value of∠ PBC? (2)
OR
Find the value of ∠ y. (2)?
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 thatit can reach at point P on the pole and this should make 60° with line AC.
9. Show thatΔ APC and Δ BPC are congruent. (1)
10. Find the value of∠ x. (1)
11. What is the value of∠ PBC? (2)
OR
Find the value of ∠ y. (2)?
Most Upvoted Answer
20 Read the following text carefully and answer the questions that fol...
1. Congruence of Triangles Δ APC and Δ BPC
To show that triangles Δ APC and Δ BPC are congruent, we can use the Side-Angle-Side (SAS) criterion for congruence:
- Common Side: Both triangles share side PC.
- Angle: The angle ∠ ACP is equal to angle ∠ BCP (both are angles formed with the pole and the horizontal line AC).
- Side Lengths: The length of AC is the same for both triangles.
Since two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, we conclude that:
- Δ APC ≅ Δ BPC.
2. Finding the Value of ∠ x
To find the value of ∠ x, we can use the fact that the sum of angles in triangle Δ APC equals 180 degrees.
- Given: ∠ ACP = 60° (as stated in the problem).
- Since Δ APC is congruent to Δ BPC, we also have ∠ BCP = 60°.
Using the angle sum property:
∠ APC + ∠ ACP + ∠ PCA = 180°
Let ∠ APC = x. Therefore:
x + 60° + 60° = 180°
Solving for x gives:
x = 180° - 120° = 60°.
Thus, ∠ x = 60°.
3. Finding the Value of ∠ PBC
To find ∠ PBC, we can analyze triangle Δ BPC:
- We already know that ∠ BCP = 60°.
- From congruence, ∠ BAP = ∠ PBC.
Using the angle sum property in triangle Δ BPC:
∠ PBC + ∠ BCP + ∠ BPC = 180°
Let ∠ PBC = y. Therefore:
y + 60° + 60° = 180°
Solving for y gives:
y = 180° - 120° = 60°.
Hence, ∠ PBC = 60°.
To show that triangles Δ APC and Δ BPC are congruent, we can use the Side-Angle-Side (SAS) criterion for congruence:
- Common Side: Both triangles share side PC.
- Angle: The angle ∠ ACP is equal to angle ∠ BCP (both are angles formed with the pole and the horizontal line AC).
- Side Lengths: The length of AC is the same for both triangles.
Since two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, we conclude that:
- Δ APC ≅ Δ BPC.
2. Finding the Value of ∠ x
To find the value of ∠ x, we can use the fact that the sum of angles in triangle Δ APC equals 180 degrees.
- Given: ∠ ACP = 60° (as stated in the problem).
- Since Δ APC is congruent to Δ BPC, we also have ∠ BCP = 60°.
Using the angle sum property:
∠ APC + ∠ ACP + ∠ PCA = 180°
Let ∠ APC = x. Therefore:
x + 60° + 60° = 180°
Solving for x gives:
x = 180° - 120° = 60°.
Thus, ∠ x = 60°.
3. Finding the Value of ∠ PBC
To find ∠ PBC, we can analyze triangle Δ BPC:
- We already know that ∠ BCP = 60°.
- From congruence, ∠ BAP = ∠ PBC.
Using the angle sum property in triangle Δ BPC:
∠ PBC + ∠ BCP + ∠ BPC = 180°
Let ∠ PBC = y. Therefore:
y + 60° + 60° = 180°
Solving for y gives:
y = 180° - 120° = 60°.
Hence, ∠ PBC = 60°.
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20 Read the following text carefully and answer the questions that follow: 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 thatit can reach at point P on the pole and this should make 60° with line AC. 9. Show thatΔ APC and Δ BPC are congruent. (1) 10. Find the value of∠ x. (1) 11. What is the value of∠ PBC? (2) OR Find the value of ∠ y. (2)?
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20 Read the following text carefully and answer the questions that follow: 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 thatit can reach at point P on the pole and this should make 60° with line AC. 9. Show thatΔ APC and Δ BPC are congruent. (1) 10. Find the value of∠ x. (1) 11. What is the value of∠ PBC? (2) OR Find the value of ∠ y. (2)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 20 Read the following text carefully and answer the questions that follow: 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 thatit can reach at point P on the pole and this should make 60° with line AC. 9. Show thatΔ APC and Δ BPC are congruent. (1) 10. Find the value of∠ x. (1) 11. What is the value of∠ PBC? (2) OR Find the value of ∠ y. (2)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 20 Read the following text carefully and answer the questions that follow: 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 thatit can reach at point P on the pole and this should make 60° with line AC. 9. Show thatΔ APC and Δ BPC are congruent. (1) 10. Find the value of∠ x. (1) 11. What is the value of∠ PBC? (2) OR Find the value of ∠ y. (2)?.
20 Read the following text carefully and answer the questions that follow: 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 thatit can reach at point P on the pole and this should make 60° with line AC. 9. Show thatΔ APC and Δ BPC are congruent. (1) 10. Find the value of∠ x. (1) 11. What is the value of∠ PBC? (2) OR Find the value of ∠ y. (2)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 20 Read the following text carefully and answer the questions that follow: 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 thatit can reach at point P on the pole and this should make 60° with line AC. 9. Show thatΔ APC and Δ BPC are congruent. (1) 10. Find the value of∠ x. (1) 11. What is the value of∠ PBC? (2) OR Find the value of ∠ y. (2)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 20 Read the following text carefully and answer the questions that follow: 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 thatit can reach at point P on the pole and this should make 60° with line AC. 9. Show thatΔ APC and Δ BPC are congruent. (1) 10. Find the value of∠ x. (1) 11. What is the value of∠ PBC? (2) OR Find the value of ∠ y. (2)?.
Solutions for 20 Read the following text carefully and answer the questions that follow: 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 thatit can reach at point P on the pole and this should make 60° with line AC. 9. Show thatΔ APC and Δ BPC are congruent. (1) 10. Find the value of∠ x. (1) 11. What is the value of∠ PBC? (2) OR Find the value of ∠ y. (2)? in English & in Hindi are available as part of our courses for UPSC.
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