Page 227 - ICSE Math 7

Construction of Triangles

We know that triangles are classified on the basis of their sides and angles.
Some important properties of triangles:

• The sum of three angles of a triangle is 180°.
• The exterior angle of a triangle is equal to the sum of interior opposite angles.
• The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
• In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the
squares of the lengths of the other two sides.

To construct a triangle when two sides and the included angle are given

Let’s construct a DABC in which AB = 4 cm, BC = 7.5 cm and ∠ABC = 45°. To do so, follow the
steps given below.

Step 1: Draw a line segment BC of length 7.5 cm. B 7.5 cm C

D

Step 2: Draw ∠CBD = 45° at B.

B 7.5 cm C

D
A
Step 3: With B as centre, draw an arc of radius 4 cm to intersect ray BD at A.

B 7.5 cm C

D
A
Step 4: Join A and C to get the required DABC.

B 7.5 cm C

To construct a triangle when two angles and one side are given

Let’s construct a DABC in which ∠A = 30°, ∠B = 60° and AB = 8.8 cm. To do so, follow the steps
given below.

Step 1: Draw a line segment AB of length 8.8 cm. A 8.8 cm B

D
Step 2: Draw ∠BAD = 30° at A.
A 8.8 cm B

E
Step 3: Draw ∠ABE = 60° at B to intersect ray AD at C. C D
D ABC is the required triangle.
A 8.8 cm B

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