Construction Of Triangles

Construction of Triangles Sketching triangles to be constructed 1. Make a rough drawing before drawing the accurate figure. 2. Write all the given data on the figure. 3. Then plan construction of the figure according to the given data. A. SSS-Triangle Construction Note: Before attempting construction of a triangle, check that the sum of any two lengths of the triangle is greater than the third side. Otherwise, the construction of the triangle is not possible. Example 1: Construct a triangle ABC in which AB = 6 cm, BC = 3 cm and CA = 5 cm Solution: Steps of construction 1. Draw a line segment AB = 6 cm 2. With B as centre and radius = 3 cm draw an arc. 3. With A as centre and radius = 5 cm, draw an arc cutting the previous arc at C. 4. Join A to C and B to C. Then ABC is the required triangle.

Example 2: Construct an equilateral triangle of side 4 cm Solution:

Steps of construction 1. Draw a line segment BC = 4 cm 2. With B as centre and radius = 4 cm draw an arc 3. With C as centre and same radius, draw another arc, meeting the first arc at A. 4. Join AB and AC

Therefore Triangle ABC is the required triangle Example 3: Construct an isosceles triangle with AB = AC = 4 cm and BC = 3 cm. Solution:

Steps of construction 1. Draw a line segment BC = 3 cm 2. With B as centre and radius = 4 cm, draw an arc. 3. With C as centre and radius = 4 cm drawn another arc, meeting the first arc at A. 4. Join AB and AC.

Therefore Triangle ABC is the required triangle B. SAS-Triangle Construction In this case, two sides and the included angle are given. Example 1: Construct a triangle ABC in which AB = 7 cm, BC = 3 cm, and ∠B = 60o Solution

Steps of construction 1. Draw AB = 7 cm 2. At B, draw an angle of 60o using compasses. 3. With B as centre and radius 3 cm, draw an arc cutting BX at C. 4. Join AC Then ABC is the required triangle. Example 2: Construct a triangle ABC with ∠B = 60o , AB = 4 cm, BC = 3 cm Solution: Steps of construction 1. Draw a line segment AB = 4 cm 2. At B, draw an angle of 90o with help of compasses. 3. With B as centre and radius 3 cm, draw an arc cutting BX at C. 4. Join AC ABC is the required triangle

Example 3: Draw a triangle ABC with ∠B = 120o AB = 3 cm, BC = 3 cm. Solution:

Steps of construction 1. Draw a line segment AB = 3 cm 2. At B, draw an angle of 120o with the help of compasses. 3. With B as centre and radius 3 cm, draw an arc cutting BX at C. 4. Join AC

ABC is the required triangle. C ASA-Triangle construction In this case two angles of the triangle and the included side are given. Example: Construct a triangle ABC in which ∠A = 45o , AB= 4 cm, and ∠B = 30o Solution:

Steps of construction 1. Draw a line segment AB of length 4 cm. 2. At A construct an angle of 45o using compasses. 3. At B, construct an angle of 30o using compasses. Let it meet AX at C. 4. Join CA ABC is the required triangle. Example 2: Construct a triangle ABC in which BC = 5 cm, ∠B = 50o and ∠45o Solution: Steps of construction

1. Draw a line segment BC = 5 cm 2. At B, make ∠CBX = 50o by using a protractor. 3. Construct ∠BCY = 45o using ruler and compasses. Let BX and CY interest at A. Then triangle ABC is the required triangle

Example 3: Construct a triangle ABC in which BC = 3m, ∠B = 110o and ∠C = 40o Solution:

Steps of construction 1. Draw a line segment BC = 3 cm 2. At B, make ∠CBX = 110o 3. At C, make ∠BCY = 40o Let BX and CY intersect at A. Then triangle ABC, is the required triangle D. RHS-Triangle construction Example 1: Construct a right triangle PQR, where ∠Q = 90o , RP = 6 cm and QR = 4 cm Solution:

Steps of construction 1. Draw a line segment QR = 4 cm 2. At point Q, draw ∠XQR = 90o 3. With R as centre and radius = 6 cm, cut RP = 6 cm 4. Join PR.

Triangle PQR is the required triangle Example 2: Construct a right triangle ABC, right angled at C in which AB = 5 cm and BC = 4 cm Solution:

Steps of construction 1. Draw BC = 4 cm 2. Make ∠BCY = 90o 3. With B as centre, and radius 5 cm, draw an arc, cutting CY at A. 4. Join AB. Now triangle ABC is the required triangle. Example 3: Construct a right triangle ABC in which hypotenuse BC = 6 cm, and the other two sides are equal. Solution: Steps of construction 1. Draw BC = 6 cm

2. Draw the perpendicular bisector BC. Let it meets BC at D. 3. Now, D is centre and radius equal to DB, draw a semicircle on BC. Let the semicircle meet XY at A. 4. Join AB and AC.

Since angle in a semicircle is a right angle, therefore, ∠BAC = 90o . Thus, Triangle ABC is the required triangle. ************************************************************