Constructing a Triangle using ASA property

Q. Which of the following criteria cannot be used to construct a unique triangle?

1. ASA
2. SSS
3. AAA
4. SAS

Q.

Construct $△\mathrm{PQR}$ in which $\mathrm{PR}=7\mathrm{cm}$ and $\mathrm{PQ}=\mathrm{QR}=5\mathrm{cm}$. Measure $\angle \mathrm{P}$ and $\angle \mathrm{R}$. What type of triangle is this?

Q. The steps to construct a $△XYZ$, in which $XY=4.5$ centimeters, $\angle X={100}^{\circ }$, and $\angle Y={50}^{\circ }$ is given below. Choose the correct order of the steps.

1. Construct a line segment $XP$ such that $\angle PXY={100}^{\circ }.$
2. Locate points $X$ and $Y$ on it such that $XY=4.5$ cm.
3. Draw a line segment that is sufficiently long using a ruler.
4. Extend $XP$ and $YQ$ to intersect at $Z$.
5. Construct a line segment $YQ$ such that $\angle XYQ={50}^{\circ }$.

1. $3,2,4,1,5$
2. $2,3,1,5,4$
3. $3,2,1,5,4$
4. $2,1,3,4,5$

Q. $△ABC$ is constructed such that $BC=5.8$ centimeters and $\angle C=\angle B={30}^{\circ }$. In this case, the sum of length of sides $AC$ and $AB$ is _________.

1. 5.4 cm
2. 4.8 cm
3. 7.2 cm
4. 6.8 cm

Q. If in $△ABC,AB=4.5\text{cm},\angle ABC={60}^{\circ },\text{and}\angle BAC={80}^{\circ }$, then which of the following options will be the length of $AC?$

1. $6.1\text{cm}$
2. $6.5\text{cm}$
3. $5\text{cm}$
4. $5.4\text{cm}$