Question

Write the truth value (T/F) of the following with suitable reasons:
(i) A circle is a plane figure.
(ii) Line segment joining the centre to any point on the circle is a radius of the circle.
(iii) If a circle is divided into three equal arcs each is a major arc.
(iv) A circle has only finite number of equal chords.
(v) A chord of a circle, which is twice as long is its radius is a diameter of the circle.
(vi) Sector is the region between the chord and its corresponding arc.
(vii) The degree measure of an arc is the complement of the central angle containing the arc.
(viii) The degree measure of a semi-circle is 180°.

Answer 1

Answer:

true, true, false, true, false, true, true

Answer 2

(i) A circle is a plane figure.

TRUE

Because circle is a two dimensional figure and it can also be referred as plain figure.  

(ii) Line segment joining the centre to any point on the circle is a radius of the circle.

TRUE  

Because all points on the circle are equidistant from the centre of the circle and this equal distances is called radius of the circle.  

(iii) If a circle is divided into three equal arcs each is a major arc.

FALSE  

Because all three arcs are equal there is no difference between the major and minor arcs.  

(iv) A circle has only finite number of equal chords.

FALSE  

Because in circle, infinitely many equal chords can be drawn.  

 

(v) A chord of a circle, which is twice as long is its radius is a diameter of the circle.

TRUE  

By definition of a diameter it is twice the radius of a circle.

 

(vi) Sector is the region between the chord and its corresponding arc.

FALSE  

Because the sector is a region between two radii and an Arc.

(vii) The degree measure of an arc is the complement of the central angle containing the arc.

FALSE

Because the degree measure of a minor arc is the measure of the central angle containing the arc and that of a major Arc is 360° minus  the degree measure of the corresponding minor arc.

 

(viii) The degree measure of a semi-circle is 180°.

TRUE

Because we know that the degree measure of a circle is 360° and semicircle is half the circle.

HOPE THIS ANSWER WILL HELP YOU…..

 

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