Q. 314.2( 5 Votes )

Draw a triangle A

Answer :

On the basis of the question, the figure can be drawn as follows:

We know that in a triangle sum of all its angles is 180o

In triangle ABC, we have

A + B + C = 180o

105o + 45o + C = 180o

C = 180o – 150o

C = 30o

Steps of construction:

(i) Firstly, draw a triangle ABC having side BC = 7 cm, B = 45o and C = 30o

(ii) Now draw a BX by making an acute angle with the side BC on the opposite side of the vertex A

(iii) After this locate 4 points on BX i.e. B1, B2, B3 and B4

(iv) Now, join B3C and then draw a parallel line through B4 to B3C which intersect the extended BC at C’

(v) From C’ draw a line parallel to AC which intersects the extended line segment at C’


From the figure, we have:

As line A’C’ is parallel to Ac, therefore, it will make the same angle with the line BC

A’C’B = ACB (Corresponding angles are equal) (i)

Now, in triangle A’B’C’ and triangle ABC we have:

B = B (Common)

A’C’B = ACB [From equation (i)]

(By AA similarity rule)

As the corresponding sides of both the similar triangles are in the same ratio

Hence, the construction is justified.

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