?A, ?F, ?G, ?D are exterior angles. ?B, ?E, ?H, ?C are interior angles. ?B and ?E, ?H and ?C are consecutive interior angles. ?A and ?G, ?F and ?D are alternate exterior angles. ?E and ?C, ?H and ?B are alternate interior angles. ?A and ?E, ?C and ?G ?D and ?H, ?F and ?B are corresponding angles.

Used to read angle if re is no protractor. To draw an angle, compasses describe an arc from origin with a radius taken from 60 mark. The required angle is copied from scale by compasses, and an arc of this radius drawn from sixty mark so it intersects first arc. The line drawn from this point to origin will be at target angle.

Hypocycloid is a special plane curve generated by trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to cycloid but instead of circle rolling along a line, it rolls within a circle. In figure below, circle with radius b rolls inside bigger circle thus making curves known as hypocycloid.

It is not possible to construct an angle that is not a multiple of 15. Angle 40 is not a multiple of 15 while 120 is multiple of 15. Angle 37.5 is formed by angular bisector of angle 75 which is again a multiple of 15. Angle 33.75 is formed by bisecting angle 135 two times, is also a multiple of 15.

Since volume is given, formula will turn as
R.F = (drawing volume/original volume)³
R.F = (216 cm³ / 1728 * (100)³ cm³)³
= 1/200.

The locus of swimmer will be a circle with light house as centre and same distance between light house and swimmer as radius (locus postulate of a circle).

When a uniform and flexible chain hangs from two pegs, its weight is uniformly distributed along its length. The shape it takes is called a catenary. The catenary curve has a U-like shape, superficially similar in appearance to a parabola, but it is not a parabola. The catenary is also called alysoid, chainette, or, particularly in materials sciences, funicular. This figure blow represents a catenary and a parabola.

Representative fractions are a unit-less relation between one ?unit? on map and however many ?units? of same type on ground. When a 1 cm long line in a drawing sheet represents 1 m length of actual object on ground, R.F is equal to 1 cm/1 m = 1/100. These are of 3 types-full scale, reduced scale and enlarged scale.

Trochoid is a curve generated by a point fixed to a circle, within or outside its circumference, as circle rolls along a straight line. The curve generated below shows us inferior trochoid.

The furlong was distance a team of oxen could plough without resting. This was standardized to be exactly 40 rods (1 rod = 51/2 yards) or one-eighth of a mile or 660 feet given by U.S unit system. Accurately one furlong = 201.168 meters.