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 60° with line AC.
Answer the following questions:
i. In the ΔPAC and ΔPBC which side is common?
a. PC
b. AB
c. AC
d. BC
ii. In the ΔPAC and ΔPBC which angles are given to be equal?
a. ∠A = ∠x
b. ∠B = ∠x
c. ∠B = ∠y
d. None
iii. In the figure, ΔPAC and ΔPBC are congruent due to which criteria?
a. RHS
b. SAS
c. SSS
d. ASA
iv. What is the value of ∠PBC?
a. 30°
b. 60°
c. 90°
d. 45°
v. What is the value of ∠x?
a. 45°
b. 60°
c. 90°
d. 30°
Answers
Question i) :- In the ΔPAC and ΔPBC which side is common?
a. PC
b. AB
c. AC
d. BC
Answer :- (a) PC .
- Perpendicular height which is pole is common .
Question ii) :- In the ΔPAC and ΔPBC which angles are given to be equal?
a. ∠A = ∠x
b. ∠B = ∠x
c. ∠B = ∠y
d. None
Answer :- (d) None .
- ∠A = ∠B .
- ∠x = ∠y .
Question iii) :- In the figure, ΔPAC and ΔPBC are congruent due to which criteria?
a. RHS
b. SAS
c. SSS
d. ASA
Answer :-
- By RHS congruence rule .
Question iv) :- What is the value of ∠PBC?
a. 30°
b. 60°
c. 90°
d. 45°
Answer :- (b) 60° .
- in ∆PAB , PA = PB => Angle opposite to equal sides are equal . therefore, ∠A = ∠B = 60°
Question v) :-What is the value of ∠x?
a. 45°
b. 60°
c. 90°
d. 30°
Answer :- (d) 30° .
- ∠x = 180° - (90° + 60°) = 180° - 150° = 30° .
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