Question 1. Steps to divide a line segment  AB in the given ratio m : n by drawing alternated angles is given. Choose the correct order.
1.Draw any ray AX making acute angle with AB and  ray BY such that $\angle BAX=\angle ABY$.
2.Locate the points $A_1,A_2,A_3...A_m$ on AX and  $B_1,B_2,B_3...B_n$ on BY such that $A{A}_1=A_1{A}_2=B{B}_1=B_1{B}_2$
3.Draw a ray BY parallel to AX by making $\angle ABY=\angle BAX$
4.Join $A_m{B}_n$.

Question 2. A line segment $AB$ is divided in the ratio $m:n$ where $m$ and $n$ are co-prime, using a single ray $AX$. The number of arcs to be drawn on $AX$ is _____.

Question 3. Match the following based on the construction of similar triangles, if scale factor $\left(\frac{m}{n}\right)$ is
$\begin{array}{cc}I.>1& a)Thesimilartriangleissmallerthantheoriginaltriangle.\\ II.<1& b)Thetwotrianglesarecongruenttriangles.\\ III.=1& c)Thesimilartriangleislargerthantheoriginaltriangle.\end{array}$

Question 4. A triangle $ABC$ with $BC=6cm,AB=5cm$ and $\angle ABC={60}^{\circ }$. The image of constructing a similar triangle of $\Delta ABC$ whose sides are $\frac{3}{4}$ times the corresponding sides of the $\Delta ABC$ is given below.

Arrange the steps of construction in the correct order.
1. Join $B_{4}C$ and raw a line through $B_3$
(the third point, 3 being smaller of 4 in $\frac{3}{4}$) parallel to $B_{4}C$  to intersect BC at C'.
2. Draw any ray $BX$ making an acute angle with BC on the side opposite to  the vertex A.
3. Locate 4 (the greater of 3 and 4 in$\frac{3}{4}$) points $B_1,B_2,B_3\text{and}{B}_4$ on BX  so that $B{B}_1=B_1{B}_2=B_2{B}_3=B_3{B}_4$
4. Draw a line through C' parallel to the line CA to intersect BA at A'.

Question 5. Construction of a $\Delta A^{\prime }{C}^{\prime }B$ similar to $\Delta ACB$ is shown in the figure below, which condition is used to construct $A^{\prime }{C}^{\prime }$ ||$AC$?

Question 6. A triangle similar to given $\Delta ABC$with sides equal to $\frac{3}{4}$ of the sides of $\Delta ABC$ is to be constructed as the given image. Arrange the following steps of construction in order:
1. Join $B_{4}C$ and raw a line through $B_3$( the third point, 3 being smaller of 4 in$\frac{3}{4}$) parallel to $B_{4}C$  to intersect BC at C'.
2. Draw any ray BX making an acute angle with BC on the side opposite to  the vertex A.
3. Locate 4(the greater of 3 and 4 in$\frac{3}{4}$) points $B_1,B_2,B_3\text{and}{B}_4$ on BX  so that $B{B}_1=B_1{B}_2=B_2{B}_3=B_3{B}_4$
4. Draw a line through C' parallel to the line CA to intersect BA at A'.

Question 7. Image of the division of line segment AB in the ratio 3:2 is given below.

$\angle BAX$ is a/an :

Question 8. A triangle similar to given $\Delta ABC$with sides equal to $\frac{3}{4}$ of the sides of $\Delta ABC$ is constructed.

$\frac{B{C}^{\prime }}{BC}$ is equal to____.

Question 9. AA postulate is used to prove the similarity of the constructed triangle.

Question 10. The ratio of $\frac{BC}{C{C}^{\prime }}$ is 3:5. What will the ratio of corresponding sides be if triangles ABC and A'BC' are similar? Given that BC and BC' lie
on the same ray BY.