Question 7
Construct at least 4 different angles. Draw their bisectors.
An angle bisector is a line that divides an angle into two equal parts.
Step 1 — Drawing Four Angles
We will draw four different angles. Let us use a ruler and pencil. First, draw two lines meeting at a point. This forms an angle. Let us draw angle ABC. It is an acute angle. Next, draw angle DEF. It is an obtuse angle. Then, draw angle GHI. It is a right angle. Finally, draw angle JKL. It is a straight angle.
Step 2 — Bisecting Angle ABC
We will bisect angle ABC. Place the compass point at vertex B. Draw an arc cutting arm BA at A'. It also cuts arm BC at C'. Now, place the compass point at A'. Draw an arc inside the angle. Keep the same compass width. Place the compass point at C'. Draw another arc inside the angle. These two arcs will cross. Let their intersection point be B'. Draw a ray from B through B'. This ray BB' is the bisector of angle ABC.
Step 3 — Bisecting Angle DEF
We will bisect angle DEF. Place the compass point at vertex E. Draw an arc cutting arm ED at D'. It also cuts arm EF at F'. Now, place the compass point at D'. Draw an arc inside the angle. Keep the same compass width. Place the compass point at F'. Draw another arc inside the angle. These two arcs will cross. Let their intersection point be E'. Draw a ray from E through E'. This ray EE' is the bisector of angle DEF.
Step 4 — Bisecting Angle GHI
We will bisect angle GHI. Place the compass point at vertex H. Draw an arc cutting arm HG at G'. It also cuts arm HI at I'. Now, place the compass point at G'. Draw an arc inside the angle. Keep the same compass width. Place the compass point at I'. Draw another arc inside the angle. These two arcs will cross. Let their intersection point be H'. Draw a ray from H through H'. This ray HH' is the bisector of angle GHI.
Step 5 — Bisecting Angle JKL
We will bisect angle JKL. Place the compass point at vertex K. Draw an arc cutting arm KJ at J'. It also cuts arm KL at L'. Now, place the compass point at J'. Draw an arc inside the angle. Keep the same compass width. Place the compass point at L'. Draw another arc inside the angle. These two arcs will cross. Let their intersection point be K'. Draw a ray from K through K'. This ray KK' is the bisector of angle JKL.
Answer
(i) BB' is the bisector of angle ABC. (ii) EE' is the bisector of angle DEF. (iii) HH' is the bisector of angle GHI. (iv) KK' is the bisector of angle JKL.
More questions in FIO
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Hint 2: We can draw the whole line if any two of its points are known.]
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