question_answer

Construct a \[\Delta \text{ }ABC\] in which \[AB=6\text{ }cm,\text{ }\angle A=30{}^\circ \] and \[\angle B=60{}^\circ \]. Construct another \[\Delta \text{ }AB'C\]similar to \[\Delta \text{ }ABC\]with base\[AB'=8\text{ }cm\].

Answer:

Steps of construction:

(i) Draw a line segment \[AB=6\text{ }cm\].

(ii) Construct \[\angle ABP=60{}^\circ \] and \[\angle QAB=30{}^\circ \]

(iii) Join AC and BC such that C is the intersection point of BP and AQ.

Thus, \[\Delta \,ABC\] is the required triangle.

(iv) Extend AB to B', such that \[AB'=8\text{ }cm\].

(v) Draw \[B'C'\parallel BC\] cutting AC produced at C?.

Then, \[\Delta \,AB'C'\] is the required triangle similar to \[\Delta \,ABC\].