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’



Justification:


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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