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Constructing TrianglesConstructing 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. _________________________________________________________________________ 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. _________________________________________________________________ 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) • Constructing Quadrilaterals • Constructing Triangles(when sum of sides or perimeter is given)
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