Draw diagrams illustrating each of the following situation:

(a) Three straight lines which do not pass through a fixed point.

(b) A point and rays emanating from that point such that the angle between any two adjacent rays is an acute angle.

(c) Two angles which are not adjacent angles, but still supplementary.

(d) Three points in the plane which are equidistant from each other.

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Solution

(a) Three lines, which do not pass through a fixed point, can be drawn as:

(b) The required figure is shown below.

(c) Let AB be a straight line and let PQ and RS be two parallel lines that intersect AB.

In the figure,

Therefore, angles PMN and RNM are supplementary.

(d) Let A, B and C be three points in a plane, which are equidistant to each other.

In the figure, AB = BC = AC.

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Similar questions

Q. Draw diagrams illustrating each of the following situation:
(a) Three straight lines which do not pass through a fixed point.
(b) A point and rays emanating from that point such that the angle between any two adjacent rays is an acute angle.
(c) Two angles which are not adjacent angles, but still supplementary.
(d) Three points in the plane which are equidistant from each other.

Q. Ray PR and ray PQ are perpendicular to each other. The point B is in the interior of

∠

QPR and a point A is in the exterior of

∠

RPQ such that ray PB and ray PA are perpendicular to each other. Draw the figure and write down a pair of (i) Complementary angle (ii) Supplementary angles (iii) Congruent angles.

Draw the pairs of angles as described below.If that is not possible, say why.

(i) Complementary angles that are not adjacent.

(ii) Angles in a linear pair which are not supplementary.

(iii) Complementary angles that do not form a linear pair.

(iv) Adjacent angles which are not in a linear pair.

(v) Angles which are neither complementary nor adjacent.

(vi) Angles in a linear pair which are complementary.

Answer the following questions and justify.
(i) Can two acute angles he complement to each other?
(ii) Can two obtuse angles be complement to each other?
(iii) Can two right angles he complement to each other?
(iv) Can two acute angles be supplementary?
(v) Can two obtuse angles be supplementary?
(vi) Can two right angles be supplementary?
(vii) Can two adjacent angles be supplementary?
(viii) Can two adjacent angles be complementary?
(ix) Can two obtuse angles be adjacent angles?
(x) Can an acute angle be adjacent to an obtuse angle?
(xi) Can two acute angles form a linear pair?
(xii) can two obtuse angles form a linear pair?
(xiii) Can two right angles form a linear pair?

Q. Construct the following figures.
(i) A pair of adjacent angles
(ii) Two supplementary angles which are not adjacent angles.
(iii) A pair of adjacent complementary angles.

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