# Constructing Triangles

Constructing triangles, we need three measurements.
Even we can construct a triangle when the base, one base angle and the sum of the other two sides are given or given its base, a base angle and the difference of the other two sides or given, its perimeter and two base angles. Here, I have explained you this type of construction.

1) Construct a Triangle, when its base, sum of the other two sides and one base angle are given.

Constructing triangle ABC in which AB = 5.8 cm , BC + CA = 8.4 cm and ∠B = 45°.

Step 1: Draw a line segment AB 5.8 cm.

Step 2 : Draw ∠B = 45°.

Step 3 : With Center B and radius 8.4 cm, make an arc which intersects BX at D.

Step 4 : Join D to A.

Step 5 : Draw a perpendicular bisector of segment DA it intersect the line segment BD at point C.

Step 6 : Join C to A.

ABC is the required triangle.

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2) Triangle construction, when its base, difference of the other two sides and one base angle are given.
Construct a triangle ABC in which BC = 3.4 cm , AB - AC = 1.5 cm and ∠B = 45
0 .

Step 1 : Draw a line segment BC of length 3.4cm

Step 2 : Draw an angle of 45 degree from point B

Step 3 : From Ray AX cut off the line segment BD = 1.5cm

Step 4 : Join B to C

Step 5 : Draw side bisector of DC

Step 6 : Extend side bisector of DC it intersect the Ray BX at point A

Step 7 : Join A to C, ABC is the required triangle.

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3)Construction of a Triangle of given perimeter,and two base Angles.

Using ruler and compasses only, construct a triangle ABC from the following data
AB + BC + CA = 12 cm ∠B = 45
0 and ∠C= 60°.

Step 1 : Draw a line segment XY of 12 cm

Step 2 : From point X draw ray XD at 45 degree and from point Y draw ray YE at 60 degree

Step 3 : draw angle bisector of X and Y, two angle bisectors intersect each other at point A

Step 4 : Draw line bisector of XA and AY respectively these two line bisectors intersect XY at point B and C

Step 5 : Join A to B and A to C

Step 6 : Triangle ABC is the required triangle.

Geometrical Constructions

Basic Geometric Constructions
Construction of Line Segment
Bisecting a Line Segment
Constructing Angles
Bisecting Angles
Constructing Parallel Lines
Construction of Triangle (SSS)
SAS Triangle Construction
ASA Triangle Construction
HL Triangle Construction (Rhs -construction)