Construction of Triangles Given 2 Angles and Included Side

Q.

How many triangles are possible if length of two sides and non-included angle is given, assuming that the given length is the minimum length required to form a triangle ?

1. 1

2. 2

3. 3

4. 4

Q. Question 4
Construct a triangle XYZ in which $\angle Y={30}^{\circ },\angle Z={90}^{\circ }andXY+YZ+ZX=11cm$.

Q. Select the correct statement/statements from the following:
We can construct a unique triangle when we are given the following information:

1. measure of the three angles
2. measure of 2 angles and the included side
3. measure of 2 sides and the included angle
4. measure of one angle and one side

Q. Construct triangles of the measures given below.
In ∆EFG, l(EG) = 6 cm, m∠F = 65^°, m∠G = 45^°

Q.

$△$XYZ is drawn with the length of side XZ being 4.7 cm. If $\angle$X is 80${}^{\circ }$ and $\angle$Z is 65${}^{\circ }$, then, the measure of $\angle$Y and the length of side YZ respectively are

1. 35${}^{\circ }$, 8 cm

2. 35${}^{\circ }$, 7.4 cm

3. 45${}^{\circ }$, 8 cm

4. 45${}^{\circ }$, 7.4 cm

Q.

You are given the measurement of the two legs of a right angled triangle. What else do you need in order to draw a triangle?

1. Length of the third side

2. Measure of one angle

3. I don't need anything else as I can easily construct the triangle from the given data.

4. Either length of one side or measure of one angle

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, the length of side AB is

1. 9.8 cm

2. 5.4 cm

3. 11 cm

4. 6.6 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

1. 40${}^{\circ }$

2. 30${}^{\circ }$

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

4. 20${}^{\circ }$

Q.

$△$ABC is drawn with the length of side AB being 4.8 cm. If $\angle$B is 35${}^{\circ }$ and $\angle$C is 65${}^{\circ }$, then, the perimeter of this triangle is

1. 18.2 cm

2. 19.8 cm

3. 20.4 cm

4. 21.1 cm

Q.

A right triangle ABC right angled at A with lengths of perpendicular sides 4 cm and 3 cm is constructed. Keeping the third side as the base, another triangle BCD is constructed such that $\angle$DBC = 40${}^{\circ }$ and $\angle$BCD = 30${}^{\circ }$. Then the perimeter of triangle BCD is

1. 11.1 cm

2. 6.1 cm

3. 8.4 cm

4. 7.7 cm

Q. Construct $△DEF$ such that $DE=5$ cm, $DF=3$ cm and $\angle EDF={90}^{\circ }$.

Q. If angle B is 90 degrees and AC is 7 cm, what information is needed to construct triangle ABC?

1. Length of BC
2. Altitude AD
3. Angle B
4. Area of ABC

Q.

$△$ABC is drawn with the length of side AB being 6 cm. If $\angle$A is 65${}^{\circ }$ and $\angle$B is 65${}^{\circ }$, then $△$ABC is

1. an isosceles triangle

2. a scalene triangle

3. an equilateral triangle

4. an obtuse angled triangle

Q.

$△$PQR is drawn with the length of side QR being 4 cm. If $\angle$Q is 35${}^{\circ }$ and $\angle$R is 70${}^{\circ }$, then, the length of the side PR is

1. 2.9 cm

2. 4 cm

3. 3.6 cm

4. 2.4 cm

Q. △ABC is constructed such that BC = 5.8 cm, ∠C= ∠B = 30⁰. Then, find the sum of the lengths of side AC and AB.

Q.

$△$ABC is drawn with the length of side BC being 9.6 cm. If $\angle$B is 25${}^{\circ }$ and $\angle$C is 110${}^{\circ }$, then the measure of $\angle$A and the length of side AC respectively are

1. 45${}^{\circ }$, 5.8 cm

2. 25${}^{\circ }$, 12.6 cm

3. 45${}^{\circ }$, 12.6 cm

4. 25${}^{\circ }$, 5.8 cm

Q. $△$XYZ is drawn with the length of side XZ being 4.7 and the length of side YZ is 8 cm. If $\angle$Z is 65${}^{\circ }$, then, what is $\angle$Y? ( in degrees)

1. 35

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 the length of the side AC is

1. 4.2 cm

2. 6.2 cm

3. 4.8 cm

4. 5.1 cm

Q.

If $△$ABC is drawn with length of side AB being 9 cm, $\angle$A being 45${}^{\circ }$ and $\angle$B being 65${}^{\circ }$, then the length of side AC is

1. 6.9 cm

2. 7.2 cm

3. 7.9 cm

4. 8.9 cm

Q. Construct an equilateral triangle whose altitude is $5$ $cm$. Then, area of the required triangle is:

1. $13.6c{m}^2$
2. $11.2c{m}^2$
3. $12.8c{m}^2$
4. $14.5c{m}^2$

Q.

Draw triangles of the following measurements.

(i) ΔPQR : PQ = 5 cm, ∠P = 65°, ∠Q = 65°

(ii) ΔABC : AB = 6 cm, ∠A = 40°, ∠B = 40°

(iii) ΔLMN : LM = 4 cm, ∠L = 90°, ∠M = 30°

(iv) ΔXYZ : XY = 5 cm, ∠X = 90°, ∠Q = 45°

Q.

Examine whether you can construct ΔDEF such that EF = 7.2 cm, m∠E =

110° and m∠F = 80°. Justify your answer.

Q. Draw a triangle ABC, with AC = 4 cm, BC = 3 cm and ∠C = 105°. Measure AB. Is (AB)² = (AC)² + (BC)²? If not, which one of the following is true:
(AB)² > (AC)² + (BC)² or (AB)² < (AC)² + (BC)²?

Q. Draw ∆ ABC in which AC = 6 cm, ∠A = 90° and ∠B = 60°.

Q. Draw a triangle ABC, with AC = 4 cm, BC = 3 cm and ∠C = 105°. Measure AB. Is (AB)² = (AC)² + (BC)²? If not, which one of the following is true:
(AB)² > (AC)² + (BC)² or (AB)² < (AC)² + (BC)²?

Q. Draw a right triangle having hypotenuse of length 5.4 cm, and one of the acute angles of measure 30°.