Practical Geome...

A line is drawn randomly in a plane. How many lines can be drawn parallel to this line that are lying in the same plane?

An angle 135^o is drawn using a compass and ruler by bisecting _________.

In the given figure, the distance between O and G is 8.5 cm. If the radius of the given circle is 3.5 cm, find the length of BG.

Two lines AB and PM intersect at a point O and the angle formed at O is 90^o.

Which of the following relationships is/are true?
1. PM ⊥ AB
2. AB || PO

Megan draws an angle of 175^o, and Garvin divides it into five equal parts. What will be the measure of two angles taken together?

A circle has ___________ end points.

The total number of angle bisectors possible for a given angle is

Alex wants to draw an angle of 165^o using a compass and ruler. Which of the following pairs of angles should he use in order to draw it successfully?

A line segment AB is trisected and hence new points, that is, P and Q are introduced on the line. Assuming P to be in between A and Q, find the length of AQ if the length of AB is 9.3 cm.

What is the purpose of a set square?

Following are the steps to construct 30^o. Find the incorrect step(s) here.

Step 1: Draw the arm PQ.
Step 2: Place the point of the compass at P and draw an arc that passes through Q.
Step 3: Place the point of the compass at Q and draw an arc that cuts the arc drawn in Step 2 at R.
Step 4: With the point of the compass still at Q, draw an arc (point T).
Step 5: With the point of the compass at R, draw an arc to cut the arc drawn in Step 4 at T.
Step 6: Join T and P. The angle QPT is 30^o.

Fill in the blanks:

A P is a special kind of segment, ray, or line that intersects a given segment at a Q angle, and passes through the given segment's R .

Arrange the following steps in the order to draw an angle bisector of a given angle.

1. With 'B' as centre, draw an arc of same radius to cut the previous arc at 'C'.
2. With 'A' as centre, draw an arc of radius more than half of AB, in the interior of the given angle.
3. With 'O' as centre, draw an arc of any radius to cut the rays of the angle at A and B.
4. Join OC. OC is the angle bisector of the given angle.
5. Construct an angle of the given measure at O using a protractor.

State T for True and F for False.

1. With a given centre, infinite circles can be drawn.
2. A single line can act as a perpendicular for two parallel lines.
3. Diagonal of a square acts like its angle bisector.

Read the following statements carefully and choose the correct option.

Statement-1: A line which bisects a given line making an angle of 90^o at the point of intersection is called perpendicular bisector.
Statement-2: The angle of 60^o can be constructed using a compass and ruler.