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.

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

ABC is the required triangle.

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Construct a triangle ABC in which BC = 3.4 cm , AB - AC = 1.5 cm and ∠B = 45

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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Using ruler and compasses only, construct a triangle ABC from the following data

AB + BC + CA = 12 cm ∠B = 45

• 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)