Construction of Triangles: When 3 Sides are Given

Q. Steps for the construction of a scalene triangle with dimensions as 6 cm, 8 cm, and 10 cm is given below. Choose the correct order.

1. To locate C which is 8 cm from A and 6 cm from B, we draw circles of 8 cm and 6 cm centered at A and B respectively using a compass.
2. Draw AB of length 10 cm using a ruler.
3. Join BC and AC to get triangle ABC.
4. The two circles meet at two different points, one on upside and other on downside. Pick any of them and name it as C.

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

Q.

An equilateral triangle has three sides that are equal in length.

1. True

2. False

Q. Question 2
Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and, say why you cannot construct them. Construct rest of the triangle.
$\begin{array}{ccccc}& Triangle& & Givenmeasurements& \\ 2.& \Delta PQR& m\angle Q={30}^{\circ }& m\angle R={60}^{\circ }& QR=4.7cm\end{array}$

Q.

Name the type of triangle given below:

• $△ABC$ with $\angle B=90°$ and $AB=BC$

Q.

State whether the triangle is right angled or not whose measures are given below:

58$°$, 83$°$, 39$°$

Q. In $△$ ABC , $\angle$ B = 90° and $\overline{AC}$ = 13 cm. Which of the following information is needed to construct the triangle?

1. $\angle$ A = 25°
2. $\overline{BC}$ = 5 cm
3. $\angle$ C = 65°
4. None of the above

Q. In $△$ ABC , $\angle$ B = 90° and $\overline{AC}$ = 13 cm. Which of the following information is needed to construct the triangle?

1. $\angle$ A = 25°
2. $\overline{BC}$ = 5 cm
3. $\angle$ C = 65°
4. None of the above

Q. Question 3
Write True or False and give reasons for your answer:

A $\Delta ABC$ can be constructed in which AB = 5cm, $\angle A={45}^{\circ }$ and BC + AC = 5cm.

Q. Which information is correct to create a 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. If the angles of a triangle are $x^{\circ }$, $2x^{\circ }$​ and $3x^{\circ }$, then the value of x is _______ .

1. ${60}^{\circ }$
2. ${15}^{\circ }$
3. ${30}^{\circ }$
4. ${90}^{\circ }$

Q. Steps for the construction of a scalene triangle with dimensions as 6 cm, 8 cm, and 10 cm is given below. Choose the correct order.

1. To locate C which is 8 cm from A and 6 cm from B, we draw circles of 8 cm and 6 cm centered at A and B respectively using a compass.
2. Draw AB of length 10 cm using a ruler.
3. Join BC and AC to get triangle ABC.
4. The two circles meet at two different points, one on upside and other on downside. Pick any of them and name it as C.

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

Q. Steps for the construction of a scalene triangle with dimensions as 6 cm, 8 cm, and 10 cm is given below. Choose the correct order.

1. To locate C which is 8 cm from A and 6 cm from B, we draw circles of 8 cm and 6 cm centered at A and B respectively using a compass.
2. Draw AB of length 10 cm using a ruler.
3. Join BC and AC to get triangle ABC.
4. The two circles meet at two different points, one on upside and other on downside. Pick any of them and name it as C.

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

Q.

Draw triangles with sides as given below.

AB = 5 cm, BC = 7 cm, CA = 8 cm

Q. Steps for the construction of a triangle ABC whose perimeter is 12cm and ratio of the sides is 2:3:4 is given below. Choose the correct order.
1.Mark point L, M, N on XZ such that XL=2cm, LM= 3 parts and MN= 4 parts
2.Join NY. Through L and M draw LB||NY and MC||NY , intersecting XY in B and C respectively.
3.Draw a line segment and locate points X and Y such that XY=12cm
4.Draw a ray XZ makes an acute angle XY and drawn in the downward direction
5.With B as centre and BX as radius draw an arc ; with C as centre CY as radius , draw an arc cutting the previous arc at A. Join AB and AC
6.From X, locate (2+3+4) =9 points at equal distance along XZ.

1. 1, 2, 3, 4, 5, 6
2. 3, 4, 6, 5, 2, 1
3. 3, 2, 4, 1, 6, 5
4. 3, 4, 6, 1, 2, 5

Q.

Which of the following information are needed to draw a unique $\Delta$ABC?

1. Length of AB and AC only

2. Length of AB, AC and BC

3. ∠A, ∠B and ∠C

4. AB, BC and ∠C

Q. In the given figure find $\angle P$ (in degrees)

Q. Which statement is true about the difference of any two sides of a triangle?

1. It is greater than the third side
2. It is zero
3. It is lesser than the third side
4. It is lesser than zero

Q.

Suppose we want to draw a triangle with one side 6 centimeters long. Which of the following pairs of lengths can be the lengths of the other two sides?

(i) 4 cm, 1 cm

(ii) 4 cm, 2 cm

(iii) 4 cm, 3 cm

(iv) 5 cm, 10 cm

(v) 5 cm, 11 cm

(vi) 5 cm, 12 cm

Q. Which information is correct to create a 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.

Which of the following information are needed to draw a unique $\Delta ABC$?

1. Length of AB and AC only

2. Length of AB, AC and BC

3. $\angle A$, $\angle B$ and $\angle C$

4. AB, BC and $\angle C$

Q. Steps for the construction of a triangle ABC with sides AB = 5 cm, BC = 4.5 cm and AC = 4 cm is given below. Choose the correct order.

1. With A as centre and radius 4 cm , draw an arc
2. Draw a line segment which is sufficiently long using ruler.
3. Join AC and BC
4. With B as centre radius 4.3 cm, draw another arc cutting the previous arc at C.
5. Locate points A and B on it such that AB = 5 cm.

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

Q.

Using which of the given measurements, a unique triangle can be constructed?

1. SSS

2. AAS

3. ASS

4. AAA

Q.

If you have three sides, you can always draw a unique triangle.

1. True

2. False

Q. A triangle has 3 sides

1. True
2. False