Question

Draw a triangle $ABC$ in which $AB=4cm,BC=6cm$ and $AC=9cm$. Construct a triangle similar to $△ABC$ with scale factor. $\frac{3}{2}$. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.

Answer 1

Step 1: Constant a triangle $ABC$ as given in the qurstion with $AB=4cm,BC=6cm$ and $AC=9cm$

Step 2: Draw a ray $AX$ making an acute angle with the base $AC$ and mark 3 points $A_1,A_2,A_3$ such that $A{A}_1=A_1{A}_2=A_2{A}_3$

Step 3: Join $A_{2}C$ and draw a line $A_3{C}^{\prime }$ such that $A_{2}C$ is parallel to $A_3{C}^{\prime }$ where $C^{\prime }$ lie on the produced $AC$

Step 4: Now draw another line parallel to $BC$ at $C^{\prime }$ such that it meet the produced $AB$ at $B^{\prime }$

Hence $\Delta A{B}^{\prime }{C}^{\prime }$ is the required triangle similar to $\Delta ABC$

The two triangles are not congruent sure all sides and all angles of both the triangle are not equal.