Construction of a Triangle with Given Perimeter and Two Base Angles

Q.

Construct a triangle $\mathrm{PQR}$ in which $\mathrm{QR}=6\mathrm{cm}$, $\angle \mathrm{Q}=60°$and $\mathrm{PR}-\mathrm{PQ}=2\mathrm{cm}$.

Q. Question 4
How many triangles can be drawn having its angles as ${45}^{\circ },{64}^{\circ }and{72}^{\circ }$? Give the reason for your answer.

Q. Consider the following statements and state which of these is/are true.
1. Area of a circle can be derived by cutting the circle into a triangle.
2. Area of a circle can be derived by dividing the circle into segments and rearranging the segments to form a rectangle.

1. Neither 1 nor 2
2. Both 1 and 2
3. 1
4. 2

Q. Construct a triangle ABC, where $\angle BAC=\angle ACB$. Let D be any point on the line AB, such that the $\angle CBD={120}^{\circ }$, AB = 3 m. [2 MARKS]