Construction of Triangles Given 2 Sides and Included Angle

Q. Draw an isosceles triangle with base 5 cm and the other sides 3.5 cm each.

Q.

Which of the following information is not sufficient a construct a unique triangle

1. The measure of two angles and included side of the triangle

2. The three sides of the triangle are 3 cm, 5 cm and 7 cm

3. Two sides and included angle of the triangle are 4 cm, 5 cm and 60⁰

4. The measure of three angles of the triangle are 50⁰, 60⁰ and 70⁰

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. In ΔRST, RS = 5 cm, and ∠SRT = 45° and ∠RST = 45°. Which criterion can be used to construct ΔRST?

1. A.S.A. criterion
2. S.A.S. criterion
3. S.S.S. criterion
4. R.H.S criterion

Q.

Construct an equilateral triangle of side 5.5 cm.

Q.

Written:

Construct a triangle ABC in which AB = 6 cm, BC = 10 cm and AC = 8 cm. Write the steps of construction.

Q.

Question 21
In which of the following cases, a unique triangle can be drawn?
a) AB = 4 cm, BC = 8 cm and CA = 2 cm
b) BC = 5.2 cm, \angle B = 90^\circ and \angle C = 110^\circ
c) XY = 5 cm, \angle X = 45^\circ and \angle Y = 60^\circ
d) An isosceles triangle with the length of each equal side 6.2 cm

Q.

$△$ABC is constructed such that AB = 7 cm, AC = 4 cm and $\angle$A = 75${}^{\circ }$. Then the length of side BC is _____ .

1. 6.8 cm

2. 7.1 cm

3. 7.4 cm

4. 7.7 cm

Q.

Construct an isosceles triangle in which the lengths of each of its equal sides is $6.5\mathrm{cm}$ and the angle between them is $110°$.

Q.

$△$XYZ is constructed such that XY = 2.5 cm, XZ = 5 cm and $\angle$X = 65${}^{\circ }$. Then $△$ABC is

1. an acute scalene triangle

2. a right scalene triangle

3. an obtuse scalene triangle

4. an acute isosceles triangle

Q.

$△$XYZ is constructed such that XY = 4 cm, XZ = 8 cm and $\angle$X = 20${}^{\circ }$. Then the difference between the lengths of sides YZ and XY is equal to

1. 1.5 cm

2. 2.5 cm

3. 3.5 cm

4. 0.5 cm

Q.

$△$XYZ is constructed such that XY = 5 cm, XZ = 4 cm and $\angle$X = 25${}^{\circ }$. Then the difference between the lengths of sides YZ and XY is equal to

1. 55${}^{\circ }$

2. 51${}^{\circ }$

3. 53${}^{\circ }$

4. 57${}^{\circ }$

Q.

$△$XYZ is constructed such that XY = 8.5 cm, YZ = 5.5 cm and $\angle$Y = 40${}^{\circ }$. Then $△$XYZ is an isosceles triangle.

1. True

2. False

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.

$△$ABC is constructed such that AB = 7 cm, AC = 4 cm and $\angle$A = 75${}^{\circ }$. Then the length of side BC is

1. 6.8 cm

2. 7.1 cm

3. 7.4 cm

4. 7.7 cm

Q. $△$ABC is drawn with the length of side BC being 9.6 cm. If $\angle$C is 36${}^{\circ }$ and $\angle$B is 84${}^{\circ }$, then, what is the length of side AB? ( in cm)

1. 6.6

Q.

Construct $\text{△XYZ}$ in which $\text{XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm}$

Q. Draw ∆ DEF such that DE = DF = 4 cm and EF = 6 cm. Measure ∠E and ∠F.

Q.

We can construct a triangle when its two angles and the __________ containing them is given.

Q.

Anubhav, a student of class VII, was asked to construct an Isosceles right triangle ABC with hypotenuse AC = 13 cm. Which of the following conclusions can help him to construct the triangle?

1. The triangle cannot be constructed at all

2. The other two angles are each of measure 60⁰

3. The other two sides are 5 cm and 12 cm

4. The other two angles are each of measure 45⁰

Q. Construct a triangle $ABC$ in which $BC=7$ cm, $\angle A={60}^{\circ }$ and altitude through $A$ is $3.7$ cm. How many such triangles are possible? Write the steps of construction.

Q.

Arav was asked to construct a triangle ABC with sides AB and BC equal to 5 cm and 6.5 cm respectively. The measure of the angle B is 60⁰. He started the construction, which of the following steps of construction followed by him is incorrect

1. With point B as centre and radius 5 cm draw an arc, which cuts line XC at point A

2. At point C draw an angle XCB = 60⁰

3. Draw a line segment BC of length 6.5 cm

4. Join AB, Triangle ABC so formed is the required triangle

Q.

Goutham took random measurements of sides i.e. AB = 3 cm, BC = 5 cm, and AC = 8.5 cm and started constructing a triangle ABC. Which of the following statement is correct?

1. Right angle triangle can be formed using these measurements.

2. Acute angle triangle can be formed using these measurements.

3. Any type of triangle can be formed using these measurements.
4. You cannot construct any type of triangle using these measurements.

Q.

Given BC = 5 cm, AC = 5.5 cm. Which of the following part is required to construct triangle ABC?

1. ∠C

2. ∠B

3. ∠A

4. None of the above

Q.

$△$ABC is constructed such that AB = 5 cm, BC = 12 cm and $\angle$B = 90${}^{\circ }$. Then AC${}^2$ = AB${}^2$ + BC${}^2$.

1. True

2. False

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

Q.

Construct a right-angled triangle ABC such that side $\overline{BC}=48cm$ and hypotenuse $\overline{AC}=50cm$.

Q. Construct a right triangle, right angled at C in which AB = 5.2 cm and BC = 4.6 cm.

Q.

$△$ABC is constructed such that AB = 7 cm, AC = 4 cm and $\angle$A = 75${}^{\circ }$. Then the length of side BC is _____ .

1. 7.1 cm

2. 7.4 cm

3. 7.7 cm

4. 6.8 cm

Q. $△$DEF is drawn with the length of side EF being 7.5 cm. If $\angle$E is 75${}^{\circ }$ and $\angle$F is 55${}^{\circ }$, then the measure of $\angle$D is ______ degrees.

1. 50