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Which of the following statements are true and which are false? Give reasons for your answers. ( i ) Only one line can pass through a single point. ( i i ) There are an infinite number of lines which pass through two distinct points. ( i i i ) A line can be produced indefinitely on both sides. ( i v ) If two circles are equal, then their radii are equal. ( v ) if A B = P Q and P Q = X Y , then A B = X Y . A ( i ) , ( i i ) - True ( i i i ) , ( i v ) , ( v ) - False B ( i ) , ( i i ) , ( i i i ) - True ( i v ) , ( v ) - False C ( i ) , ( i i ) - False ( i i i ) , ( i v ) , ( v ) - True D ( i ) , ( i i ) , ( i i i ) - False ( i v ) , ( v ) - True

Which of the following statements are true and which are false? Give reasons for your answers.
(i) Only one line can pass through a single point.
(ii) There are an infinite number of lines which pass through two distinct points.
(iii) A line can be produced indefinitely on both sides.
(iv) If two circles are equal, then their radii are equal.
(v) if AB=PQ and PQ=XY, then AB=XY.

A

(i),(ii) - True
(iii),(iv),(v) - False

B

(i),(ii),(iii) - True
(iv),(v) - False

C

(i),(ii) - False
(iii),(iv),(v) - True

D

(i),(ii),(iii) - False
(iv),(v) - True

 
 
 

Grade:12th pass

2 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
10 months ago
(i) Only one line can pass through a single point.

Answer: False

Reason: From a point infinite many lines can pass through

(ii) There are an infinite number of lines which pass through two distinct points.

Answer: False

Reason: From 2 distinct point only one straight line can pass

(iii) A terminated line can be produced indefinitely on both the sides.

Answer:True

Reason: Line segment can produced both side indefinitely and become a line.

(iv) If two circles are equal, then their radii are equal.
Answer: True

Reason: The only dimension is required to draw a circle is radius.If two radius are equal then two circle drawn ate definitely equal.

(v) In the following figure, if AB = PQ and PQ = XY, then AB = XY.

Answer: True

Reason: This is Euclid's axioms,if two things are equal ,second is equal to third then first and third will be equal.hence AB= XY
Vikas Amritiya
askIITians Faculty 158 Points
10 months ago
Dear student

(i) Only one line can pass through a single point  is false, because there are infinite lines passes through a single point.

 
(ii) There are an infinite number of lines which pass through two distinct point is false, because through two distinct point only one line can pass .
 
(iii) A terminated line can be produced indefinitely on both sides is true, because a line can be extended from both sides.
 
(iv) If two circle are equal then their radii are equal  is true, because if two circle are equal then their center is coincide and inscribe equal area thus their radii are equal.
 
(v) True, according to Euclid's First Axiom, "Things which are equal to the same thing are equal to one another".
 
 
Best wishes

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