POINTS LINES AND PLANES

Example 1 :

Look at the figure given below and answer the questions.

(i) Name three points that are collinear.

(ii) name four points that are coplanar.

(iii) Name three points that are not collinear.

Solution :

Solution (i) :

Points D, E and F lie on the same line. So they are collinear.

Solution (ii) :

Points D, E, F and G lie on the same plane. So they are coplanar. D, E, F and H are coplanar, even though the plane containing them is not drawn.

Solution (iii) :

There are many correct answers. For instance, points H, E and G do not lie on the same line.

Example 2 :

Draw three non collinear points, J, K and L. Then draw the lines JK, KL and LJ.

Solution :

Step 1 :

Draw the points J, K and L as given below.

Step 2 :

Draw the line JK by connecting the points J and K as given below.

Step 3 :

Draw the line KL by connecting the points K and L as given below.

Step 4 :

Draw the line LJ by connecting the points L and J as given below.

Example 3 :

Draw two lines, label points on the lines and name two pairs of opposite rays.

Solution :

Points M, N and X are collinear and X is between M and N.

So, XM and XN are opposite rays.

Points P, Q and X are collinear and X is between P and Q.

So, XP and XQ are opposite rays.

Example 4 :

Sketch the figure described.

"A line that intersects a plane in one point"

Solution :

(i) Draw a plane and a line.

(ii) Mark the point where they meet.

Dashes indicate where the line is hidden by the plane.

Example 5 :

Sketch the figure described.

"Two planes that intersect in a line"

Solution :

(i) Draw two planes.

(ii) Mark the line where they meet.

Dashes indicate where one plane is hidden by the other plane.

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