Constructing a Triangle using SAS property

Q. Which of the following statements is correct?

Statement 1: It is possible to construct a unique triangle when the measurements of two sides and the non-included angle are given.

Statement 2: It is possible to construct a triangle when the measurements of two sides and the included angle are given.

1. Both the statements are incorrect.
2. Statement 2 is correct and statement 1 is incorrect.
3. Both statements are correct.
4. Statement 1 is correct and statement 2 is incorrect.

Q. The steps to construct a $△PQR$, where $PQ=4cm,QR=5.2cm$, and $\angle Q={60}^{\circ }$ is given below. Choose the correct order.

1. Draw a line segment that is sufficiently long using a ruler.
2. At $Q$, construct a line segment $QM$, which is sufficiently large such that $\angle MQR={60}^{\circ }$.
3. Locate points $Q$ and $R$ on it such that $QR=5.2$ cm.
4. With $Q$ as the center and a radius of $4$ cm, draw an arc cutting $QM$ at $P$ and join $PR$.

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

Q. Construct a $\angle ABC$ , where $AB=2.7\text{cm},BC=3.7\text{cm}$, and the right angle is at $B$. Also, find the approximate length of the side $AC$.

1. $3.2\text{cm}$
2. $4\text{cm}$
3. $3.8\text{cm}$
4. $4.6\text{cm}$

Q. In a right triangle $ABC$ of area $6c{m}^2,AB\text{and BC}$ are perpendicular sides. The length of $AB$ is $3\text{cm}$. Construct a triangle and find its perimeter.

1. $12\text{cm}$
2. $15\text{cm}$
3. $10\text{cm}$
4. $20\text{cm}$

Q. In an isosceles $△ABC,AB=BC=4.5\text{cm, and}\angle BAC={30}^{\circ }$. What will be the perimeter of the triangle?

1. $16\text{cm}$
2. $23.4\text{cm}$
3. $15.2\text{cm}$
4. $16.8\text{cm}$

Q. In a $\Delta ABC$ of area 12 square centimeters, AB and BC are perpendicular sides. The length of AB is 6 centimeters. Which of the following options is true?

1. $AC=7.2\text{cm}$ and Perimeter of $\Delta ABC=17.2\text{cm}$
2. $AC=7.2\text{cm}$ and Perimeter of $\Delta ABC=10.2\text{cm}$
3. $AC=7\text{cm}$ and Perimeter of $\Delta ABC=17.2\text{cm}$
4. $AC=6.2\text{cm}$ and Perimeter of $\Delta ABC=17.2\text{cm}$

Q. A right triangle, $△ABC$ has an area of $12c{m}^2$ . Which of the following is the possible length of side $AC$ if $AB$ and $BC$ are the perpendicular sides?

1. $42.02\text{cm}$
2. $2.71\text{cm}$
3. $8.5\text{cm}$
4. $21.17\text{cm}$

Q. A carpenter wants to make a triangular table top using two sides and one angle. The two sides of the table should be $24\text{units and}8\text{units}$ and the angle between the two sides is ${30}^{\circ }$. Identify the correct sequence of the steps to construct the triangle.

1. Draw an angle ${30}^{\circ }$ with the vertex at $A$.

2. Draw $AB=3$ units.

3. Set the scale as $1$ units = $8\text{units}$.

4. Cut an arc of radius $1$ in with $A$ as the center.

5. Join $BC$.

6. Name the third point.

Q. If $AB=3$ centimeters, $AC=5$ centimeters and $\angle B=30°$, why can $△ABC$ not be constructed uniquely with $AC$ as base?

1. The vertex A coincides with the vertex C
2. Two sides and the included angle is given
3. The other two angles are not given
4. The vertex B cannot be uniquely located

Q. A triangular table needs to be made. The two sides of the table should be $15\text{ft and}5\text{ft}$, respectively, and the angle between the two sides is ${30}^{\circ }$. Identify the correct sequence of steps to construct the triangle.

1. Draw an angle ${30}^{\circ }$ with the vertex at $A$.

2. Draw $AB=3$ in.

3.Set the scale as $1$ in = $5\text{ft}$.

4. Cut an arc of radius $1$ in with $A$ as the center.

5.Join $BC$.

6.Name the third point.

1. $3-6-1-4-2-5$
2. $3-2-1-4-6-5$
3. $3-6-1-4-2-5$
4. $3-2-1-5-6-4$

Q. In $\Delta PQY,\angle P={50}^{\circ }$. If $PQ=3\text{cm}$ and $PY=3.5\text{cm}$, how many such triangles are possible?

1. Infinite
2. One
3. Two
4. Cannot be determined

Q. In $△ABC,AB=AC=4.5\text{cm, and}\angle BAC={72}^{\circ }$ lies inside a regular pentagon such that the side $BC$ is one of the sides of the pentagon. What will be the perimeter of the pentagon?

1. $26.5\text{cm}$
2. $22.5\text{cm}$
3. $29.5\text{cm}$
4. $25.7\text{cm}$