# 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.

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

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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)

• Constructing Quadrilaterals

• Constructing Triangles(when sum of sides or perimeter is given)

• 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)