Constructions

Construction of Triangles

Constructions of Triangles: Triangles are basic shapes that we come across in our day to day life. You are always surrounded by them. The slice of pizza, the hill nearby, the roof of your house are all triangles. Let us now study the constructions of triangles.

Suggested Videos

Play
Play
Play
previous arrow
next arrow
previous arrownext arrow
Slider

 

What are Triangles?

A triangle is a simple closed curve or polygon which is created by three line-segments. In geometry, any three points, specifically non-collinear, form a unique triangle and separately, a unique plane (known as two-dimensional Euclidean space). The basic elements of the triangle are sides, angles, and vertices. Let’s start with the constructions of triangles.

Browse more Topics under Constructions

Constructions of Triangles

1. Construct a scalene triangle when the base, one base angle and the sum of the lengths of the other two sides are given.

Constructions of Triangles

Construction:

  1. Draw the base BC and at the point, B makes an angle, say XBC equal to the given angle.
  2. Cut a line segment BD equal to AB + AC from the ray BX.
  3. Join DC and make an angle DCY equal to BDC.
  4. Let CY intersect BX at A
  5. ABC is the required triangle.
  6. In triangle ACD, ∠ACD = ∠ ADC
  7. So, AB = BD – AD = BD – AC
  8. AB + AC = BD

2. Construct a scalene triangle when the base, one base angle and the difference between the lengths of the other two sides are given.

Constructions of Triangles

Case 1: Let AB > AC that is AB AC is given

  1. Draw the base BC and at point B make an angle say XBC equal to the given angle.
  2. Cut the line segment BD equal to AB and  AC from ray BX.
  3. Join DC and draw the perpendicular bisector, say PQ of DC.
  4. Let it intersect BX at a point A. Join AC.

Case 2: Let AB < AC that is AC AB is given

  1. Draw the base BC and at point B make an angle say XBC equal to the given angle
  2. Cut the line segment BD equal to AC AB from the line BX extended on opposite side of line segmentBC.
  3. Join DC and draw the perpendicular bisector, sayPQ of DC.
  4. Let PQ intersect BX at A. Join AC

3. Construct a scalene triangle, given its perimeter and its two base angles.

Constructions of Triangles

  1. Draw a line segment, say XY equal to BC + CA + AB.
  2. Make angles LYX equal to B and MYX equal to C.
  3. Bisect LYX and MYX. Let these bisectors intersect at a point A
  4. Draw perpendicular bisectors PQ of AX and RS of AY.
  5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC

Then ABC is the required triangle

Solved Examples for You

Question 1: For constructing a triangle whose perimeter and both base angles are given, the first step is to:

  1. Draw base of any length
  2. Draw base of any length  = Perimeter
  3. To draw the base angles from the random line
  4. Draw base of length = 1/3 × perimeter

Solution: B is the correct option. For constructing a triangle whose perimeter and both base angles are given, the first step is to draw the base of any length  = Perimeter.

Question 2: For constructing a triangle when the base, one base angle and the difference between lengths of the other two sides are given, the base length is equal to:

  1. The difference between the length of the other two sides.
  2. Given base length
  3. The largest side
  4. None of these

Solution: B is the correct option. Here the base length is equal to the given base.

Share with friends

Customize your course in 30 seconds

Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
tutor
tutor
Ashhar Firdausi
IIT Roorkee
Biology
tutor
tutor
Dr. Nazma Shaik
VTU
Chemistry
tutor
tutor
Gaurav Tiwari
APJAKTU
Physics
Get Started

Leave a Reply

avatar
  Subscribe  
Notify of

Download the App

Watch lectures, practise questions and take tests on the go.

Customize your course in 30 seconds

Which class are you in?
No thanks.