Notes of chapter: Constructions are presented below. Indepth notes along with worksheets and NCERT Solutions for Class 9.
Step 2-
Now, draw two arcs from points E and D with radius more than ED.
Step 3-
Both arcs will intersect at point F. Join F and B.
BF is required bisector of angle ABC.
(ii) To construct the perpendicular bisector of a given line segment.
Given – Line segment AB.
What to construct – Perpendicular bisector of the line segment AB.
Steps of Construction –
Step 1-
Draw a line segment AB.
Step 2 –
Draw two arcs from points A and B as centres with radius more than half of the line segment AB.
Step 3-
Draw arcs both sides of the line segment AB
Step 4 –
These arcs intersect each other at points C and D.
Step 5 –
Join C and D. CD intersects AB at point E.
CD is our required perpendicular bisector of line segment AB.
Justification –
Join A to C and D.
Join B to C and D.
(iii) To construct an angle of 600 at the initial point of a given ray.
Given – A ray AB with initial point A.
What to construct – Draw an angle of 600 at initial point A.
Steps of Construction –
Sep 1-
Draw a ray AB with A as initial point.
Step 2-
Draw an arc of any radius which intersect ray AB at point D.
Step 3-
Draw an arc with same radius from point D as centre which intersect previous arc at point E.
Justification –
Join E and D.
Step 2-
Cut a line segment BD of measure AC + BC from the ray EA.
Step 3-
Join DB.
Step 4 –
Draw an angle DBF equal to angle ADB.
Step 5 –
Ray BF intersects ray AE at point C.
Therefore, ABC is a triangle.
Step 2-
Draw an angle EAB.
Step 3-
Cut a line segment AD equal to AC – BC from AE.
Step 4-
Join D to B.
Step 5-
Draw perpendicular bisector PQ of DB.
Step 6-
Let PQ intersect AE at point C.
Therefore, ABC is required triangle.
Justification –
CD = BC (C lies on the perpendicular bisector of DB)
AD = AC – DC
= AC – BC
Hence, proved.
Step 2-
Draw an angle EAB.
Step 3-
Cut a line AD segment BC – AC from AE.
Step 4 –
Join D to B.
Step 5 –
Draw perpendicular bisector PQ of DB.
Step 6 –
Let PQ intersect AE at point C.
Therefore, ABC is required triangle.
Justification –
CD = BC (C lies on the perpendicular bisector of DB)
AD = DC – AC
= BC – AC
Hence, proved.
(ii) To construct a triangle, given its perimeter and its two base angles.
Given – Perimeter of triangle ABC = AB + BC + CA,
Two base angles B and C.
What to construct – A triangle ABC.
Steps of Construction –
Step 1 –
Draw a line segment XY equal to perimeter AB + BC + CA.
Step 2-
Draw angle LXY equal to B and MYX equal to C.
Step 3-
Draw bisectors of angle LXY and angle MYX. Let these bisectors intersect at point A.
Step 4-
Draw perpendicular bisector PQ of AX and RS of AY.
Step 5-
Let PQ intersect XY at point B and RS intersect XY at point C.
Step 6 –
Join AB and AC.
Helping Topics