CLASS-6
CONSTRUCTION OF TRIANGLE

CONSTRUCTION OF TRIANGLE -

Constructing triangles involves various methods depending on the given information. Here are the steps to construct different types of triangles:

A. Constructing a Triangle Given Three Sides:-

  • Given the lengths of all three sides, you can use the following steps:
  1. Draw one of the sides to act as the base.
  2. From each endpoint of the base, use a compass to measure and mark the lengths of the other two sides.
  3. Connect the marks with straight lines. The intersection of these lines will form the vertex of the triangle.

B. Constructing a Triangle Given Two Sides and an Included Angle (SAS):-

  • Given the lengths of two sides and the measure of the angle between them, you can use the following steps:
  1. Draw one of the sides to act as the base.
  2. Use a protractor to measure and mark the given angle at one endpoint of the base.
  3. From the other endpoint of the base, use a compass to measure and mark the length of the second side.
  4. Connect the marks with a straight line to form the triangle.

C. Constructing a Triangle Given Two Angles and an Included Side (ASA):-

  • Given the measures of two angles and the length of the side between them, you can use the following steps:-
  1. Draw one side of the triangle.
  2. Use a protractor to measure and mark one of the given angles at one endpoint of the side.
  3. Use a protractor to measure and mark the second given angle from the first marked angle.
  4. Measure and mark the length of the side between the two marked angles.
  5. Connect the marks with straight lines to form the triangle.

D. Constructing a Triangle Given Three Angles (AAA):-

  • Given the measures of all three angles, you can't uniquely determine the triangle's size. However, you can draw a triangle that satisfies the given angle measurements by using a protractor to measure and mark each angle, then connecting the marks to form a triangle.



Here are the steps to construct different types of triangles using a straightedge (ruler) and a compass:-

Equilateral Triangle Construction:- 

Given:- The length of one side a.

Steps:-

  1. Draw a line segment AB of length a.
  2. With A and B as centres, draw arcs of the same radius using the compass.
  3. The intersection point of these arcs will be point C.
  4. Connect C to A and B to form the equilateral triangle ABC.


Isosceles Triangle Construction:-

Given:- The lengths of two equal sides a and the angle between them θ.

Steps:-

  1. Draw a line segment AB of length a.
  2. Construct the angle θ at point A using a protractor.
  3. From point B, draw an arc with radius a such that it intersects the angle bisector of angle θ at point C.
  4. Connect C to A and B to form the isosceles triangle ABC.


Scalene Triangle Construction:-

Given:- The lengths of all three sides a, b, and c.

Steps:-

  1. Draw a line segment AB of length a.
  2. From point B, construct an angle equal to the angle whose adjacent side is of length b and opposite side is of length a.
  3. From point A, draw an arc with radius b and from point B, draw an arc with radius a.
  4. Let the point of intersection of these arcs be C.
  5. Connect C to A and B to form the scalene triangle ABC.


If the sum of the length s of any two sides is less than the length of the third side, then no triangle can be drawn.

1) The length of two sides and the size of the included angle between them.

2) The length of one side and the size of any two angles.

Construction.1) To construct a triangle, when the length of three sides are given. Construct a triangle ABC such that AB = 4.5 cm, BC = 6 cm, and CA = 4.8 cm

Ans.) 

Geometry

Steps Of Construction:-

Step.1) Draw line segment BC = 6 cm, 

Step.2) With B as centre and radius 4.5 cm (= AB), draw an arc.

Step.3) With C as centre and radius 4.8 cm (= CA), draw another arc to cut the previous arc at A.

Step.4) Join AB & AC. Then ABC is the required triangle.



We can start with any side but usually we start with the longer side.

Construction.2) To construct a triangle when the lengths of two sides and the size of the included angle is given. Construct a triangle such that AB = 5.8 cm, AC = 5.2 cm, and ∠A = 60⁰ by using ruler and compass.

Geometry

Steps Of Construction -

Step.1) Draw line segment AB = 5.8 cm.

Step.2) At A, construct ∠BAP = 60⁰ by using ruler and compass

Step.3) With A as centre and radius 5.2 cm, draw an arc to meet AP at C.

Step.4) Join BC, then ABC is the required triangle.



Construction.3) To construct a triangle when the length of one side and the size of two angles are given. Construct a triangle ABC such that BC = 601 cm, ∠B = 50⁰, and ∠C = 70⁰.

Geometry

Steps Of Construction:-

Step.1) Draw line segment BC = 6.1 cm.

Step.2) At B, construct ∠PBC = 50⁰ (using ruler and compass)

Step.3) At C, construct ∠QCB = 70⁰ (using ruler and compass)

Step.4) Let BP & CQ intersect at A, then ABC is the required triangle.



Contruction.4) Construct a triangle ABC such that AB = 6.5 cm, ∠A = 60⁰ and ∠B = 45⁰ by using ruler and compass.

Geometry

Steps Of Construction:-

Step.1) Draw line segment AB = 6.5 cm.

Step.2) At A, construct ∠PAB = 60⁰ (using ruler and compass)

Step.3) At B, construct ∠QBA = 45⁰ (using ruler and compass)

Step.4) Let AP & BQ intersect at C, then ABC is the required triangle.