Construction of a Triangle with SAS Criterion

Q.

The smallest polygon that can be formed is known as a ___.

Q. Draw an angle of 60° using ruler and compasses and divide it into four equal parts. Measure each part.

Q.

Answer the following:
(a) Identify three triangles in the figure.

(b) Write the names of seven angles.

(c) Which two triangles have ∠B as common?

Q. Given two sides and an angle, a triangle can be formed.

1. included
2. excluded
3. interior

Q. In the given diagram(not drawn to scale), $PQ$ and $RS$ are straight lines, which of the following statements is true?

1. $\angle f=\angle d$
2. $\angle a+\angle b=\angle f+\angle e$
3. $\angle c=\angle e$
4. $\angle b+\angle c=\angle e+\angle f$

Q. If $AB=3$ centimeters, $AC=5$ centimeters and $\angle B={30}^{\circ }$, why can $\Delta ABC$ not be constructed uniquely with $AC$ as base?

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

Q. In $△$ XYZ , $\overline{XY}$ =6.3 cm and $\overline{XZ}$ = 7 cm. Which is the correct information needed to construct the triangle?

1. $\angle$ X = 85°
2. $\angle$ Y = 50°
3. $\angle$ Z = 45°
4. None of the above

Q.

In an isosceles $\Delta ABC$, $\angle A$ is ${30}^{\circ }$. The sides AB and AC are equal. Using constructions, find which side of $\Delta ABC$ is the shortest.

1. AC

2. AB

3. Data Insufficient

4. BC

Q. Given AB = 3 cm, AC = 5 cm and $\angle B={30}^{\circ }$, $\Delta$ABC cannot be uniquely constructed, with AC as base, why?

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

Q. Which angle of $△$POQ corresponds to $\angle$OSR of $△$ROS ?

1. $\angle$OQP
2. $\angle$QPO
3. $\angle$POQ
4. None of the above

Q.

For constructing a triangle, we must know two sides and included angle. Which triangle can be uniquely constructed by knowing two sides and any other angle?

1. Isosceles triangle

2. Equilateral triangle

3. Right angled triangle

4. Scalene triangle

Q. In $△$ CDE , $\angle$ C = 30° and $\overline{CD}$ = 8 cm. Which is the correct information needed to construct the triangle?

1. $△$ CDE is an isosceles triangle with base $\overline{DE}$
2. $△$ CDE is right angled at $\angle$E
3. $\overline{DE}$ = 11 cm and $\angle$ E = 80°
4. None of the above

Q. By which congruence rule are triangle PRQ and triangle TRS congruent?

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