Construction of Triangle When Two Sides and Included Angle is Given

Q.

Q. Construct a triangle PQR, given that PQ = 5 cm and $\angle QPR={60}^{\circ }$and $\angle QRP={45}^{\circ }$. [3 MARKS]

Q. $△$ABC is constructed such that AB = 7 cm, BC = 9 cm and $\angle$B = 55${}^{\circ }$. Then, the measure of $\angle$A is

1. 75${}^{\circ }$
2. 55${}^{\circ }$
3. 85${}^{\circ }$
4. 30${}^{\circ }$

Q. Steps of construction of traingle from two sides of 4 cm and 7 cm and included angle of 30${}^{\circ }$ are

1. $JoinC,B$
2. $Mark30degreesatA$
3. $Draw7cmarcfromA$
4. $MarkintersectionasC$
5. $DrawlineABof4cm$

Q. Which of the following triangle can be constructed when the measurement of all angles of the triangle are equal and measurement of only one side is given?

1. Right angle triangle
2. Scalene Triangle
3. Isosceles triangle
4. Equilateral triangle

Q. A triangle can be constructed if the measure of two side and angle is given.

1. included
2. adjacent
3. Complementary
4. exterior

Q.

$△$ABC is constructed such that AB = 5 cm, AC = 5 cm and $\angle$B = 50${}^{\circ }$.

Statement A: $\angle$C = $\angle$A

Statement B: $\angle$C + $\angle$B = 100${}^{\circ }$

1. Both Statement A and Statement B are false.

2. Both Statement A and Statement B are true.

3. Statement A is true and Statement B is false.

4. Statement A is false and Statement B is true.

Q.

If measure of one side is given, which of the following triangle can be constructed?

1. Scalene triangle

2. Right-angled triangle

3. Equilateral triangle

4. Isosceles triangle

Q.

$△$ABC is constructed such that AB = 5 cm, BC = 7 cm and $\angle$B = 50${}^{\circ }$. Then, the measure of $\angle$A is

1. 45${}^{\circ }$

2. 85${}^{\circ }$

3. 50${}^{\circ }$

4. 76${}^{\circ }$

Q. Write all the steps of construction of traingle from two sides of 4 cm and 7 cm and an included angle of 30⁰.

Q. Which of the following information is sufficient for construction of a unique triangle?

1. An equilateral triangle with side 6 cm
2. A right angled triangle with two other angles measured 40° and 50°
3. $\overline{AB}$ = 5 cm , $\angle$ A = 35°, $\angle$ C = 75°
4. An isosceles triangle with equal sides 5 cm

Q. Which of the following criteria is/are required for the construction of an isosceles triangle ?

1. Measurement of base angles and base side length
2. Measurement of three sides out of which two are equal.
3. Measurement of two sides and non included angle
4. Measurement of one side and hypotenuse of a right angle triangle

Q.

Construct ΔABC, given m∠A = 60°, m∠B = 30° and AB = 5.8 cm.

Q. Vikash followed the following steps to construct a triangle $△$XYZ such that XY = 6 cm, $\angle$X = 30${}^{\circ }$ and $\angle$Y = 100${}^{\circ }$


Step 1:
Draw the line segment XY of length 6 cm.

Step 2:
Draw the ray XP making an angle 30${}^{\circ }$ at X.

Step 3:
The ray XP and YQ intersects.

Step 4:
Mark the intersecting point as Z.

Step 5:
Join X, Y and Z to get the required $△$XYZ.

Which of the step is missing for constructing this $△$ABC?

1. Draw the ray YQ making an angle 100${}^{\circ }$ at Y.
2. Draw the ray XQ making an angle 100${}^{\circ }$ at X.
3. 
   Draw the ray XQ making an angle 60${}^{\circ }$ at X.
4. Draw the ray YQ making an angle 60${}^{\circ }$ at Y.

Q. Construct $\Delta RUN$ in which RN = 5cm, $\angle R=\angle N=45°.$ Measure the other angle and other sides. Name the triangle.

Q.

Construct $△\mathrm{PQR}$ in which $\mathrm{PQ}=5.3\mathrm{cm}$, $\angle \mathrm{P}=60°$ and $\angle \mathrm{Q}=30°$. Measure $\angle \mathrm{R}$. What kind of triangle is this?

Q. $△$ABC is constructed such that AB=AC= 3 cm and $\angle$A = 120${}^{\circ }$. Then the difference of measures of $\angle$A and $\angle$C is equal to

1. 60${}^{\circ }$
2. 90${}^{\circ }$
3. 30${}^{\circ }$
4. 45${}^{\circ }$

Q. $△$ABC is drawn with the length of side AB being 4 cm. If $\angle$A is 75${}^{\circ }$ and $\angle$C is 55${}^{\circ }$, then the sum of the other two sides of the $△$ABC is

1. 9.2 cm
2. 12.4 cm
3. 7.2 cm
4. 6.2

Q.

Construct $△\mathrm{PQR}$ in which $\mathrm{PQ}=5.2\mathrm{cm}$, $\mathrm{QR}=5.2\mathrm{cm}$, and $\angle \mathrm{Q}=30°$. Measure $\angle \mathrm{R}$. What type of triangle, according to sides, is this ?

Q. Construct the right angled $△PQR$ where $m\angle Q={90}^o$, $QR=8cm$ and $PR=10cm$.

Q. Construct an obtuse-angled triangle which has a base of $5.5cm$ and base angles of ${30}^{\circ }$ and ${120}^{\circ }$.
[5 marks]

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. Which of the following information is sufficient for construction of a unique triangle?

1. $\overline{AB}$ = 5 cm , $\angle$ A = 35°, $\angle$ C = 75°
2. An equilateral triangle with side 6 cm
3. A right angled triangle with two other angles measured 40° and 50°
4. An isosceles triangle with equal sides 5 cm

Q.

$△$XYZ is constructed such that XY = 5 cm, XZ = 8.5 cm and $\angle$X = 75${}^{\circ }$. Then $△$XYZ is

1. an obtuse scalene triangle

2. an acute isosceles triangle

3. a right scalene triangle

4. an acute scalene triangle

Q.

$△$XYZ is constructed such that XY = 4 cm, XZ = 8 cm and $\angle$X = 20${}^{\circ }$. Then, the sum of measures of $\angle$Y and $\angle$X is equal to

1. 38${}^{\circ }$

2. 162${}^{\circ }$

3. 160${}^{\circ }$

4. 142${}^{\circ }$

Q. Using ruler and compasses only, construct a $△ABC$ having given $\angle ABC={60}^0,\angle ACB={45}^0$ and the perpendicular from $A$ to $BC$ equal to $2.5$ cm. The length of $AB$ is

1. $2.1$ cm
2. $4.2$ cm
3. $2.9$ cm
4. $3.5$ cm

Q.

A triangle $XYZ$can be constructed when $XY=6cm$ $m\angle ZXY={40}^o$and $m\angle XYZ={100}^o$by using _____________ criterion.

1. $SAS$

2. $ASA$

Q. $△$ABC is drawn with the length of side AB being 6.5 cm. If $\angle$A is 20${}^{\circ }$ and $\angle$C is 130${}^{\circ }$, then find the length of the side AC.