Construction of Triangle Solved Questions

Question 1: Construct △XYZ, angle X = 50^o, angle Y = 70^o, and YZ = 7cm.

Solution:

Triangle XYZ

Draw a line segment YZ = 7cm

At point Y, use a protractor to draw an angle Y = 70^o

At point Z, use a protractor to draw an angle (where the line Y and Z meet) and mark the joining point as X = 50^o

Measure 7cm along the ray extending from X (towards the interior of angle X) to point Z.

Connect point X and Z.

△XYZ is constructed.

Question 2: Construct a triangle ABC, where AB = 6cm, BC = 5cm, and angle B=60^o

Solution:

Triangle ABC

Draw a line segment AB = 6cm.

At point B, use a protractor to draw angle B = 60^o

Using a ruler, mark the point 5cm along the ray extending from B (towards the interior of angle B) to point C.

Connect points A and C.

The △XYZ is constructed.

Question 3: Draw an isosceles triangle ABC with two sides of the triangle equal to 6 units and one side equal to 5 units.

Solution:

Triangle ABC

Using a ruler and a pencil draw a line segment AB = 5cm.

Put the compass at B and draw an arc with a length of 6cm above the line C.

Now, put the compass at A and draw an arc with the same measure of 6cm.

So that the arcs should intersect at point C.

Now, join the Points AB and AC to form an isosceles triangle ABC.

Question 4: Construct a triangle XYZ with XZ = 8cm. ∠X = 45^o and ∠Y = 65^o.

Solution:

Triangle XYZ

Use a ruler and draw a horizontal line of length 8cm. Mark X and Y on both sides of the line.

Put the center of the protractor on X and mark it as point Z.

Now place the center of the protractor on Y and look for 65^o in the protractor.

Join XZ and YZ

We formed an acute-angled triangle with the given angles.

Question 5: Construct a triangle LMN, given that LM = 7cm, MN = 9cm, and angle M = 45^o

Solution:

Triangle LMN

Draw a line segment LM = 7cm

At point M, draw angle M = 45^o

Measure 9cm along the ray extending from N (towards the interior of angle M) to point N.

Connect points L and N.

△LMN is constructed.

Question 6: Construct a triangle XYZ, XY = 10cm, YZ = 8cm, and angle X = 30^o

Solution:

Triangle XYZ

Draw a line segment XY = 10cm.

At point X, draw angle X = 30^o

Use the Law of Sines to find the length of side XZ:

XZ/sin X = XY/sin Y

XZ/ sin 30^o = 10/sin 60^o

XZ = 10×sin 30^o/sin 60^o

XZ = 5√3cm

Measure approximately 5√3cm along the ray extending from X (towards the interior of angle X) to point Z.

Connect points Y and Z.

△XYZ is constructed.

Question 7: Construct a triangle UVW, where VW = 12cm, UW = 15cm, and ∠U = 50^o

Solution:

Triangle UVW

Draw a line segment VW = 12cm

At Point V, draw angle V = 50^o

UV^{2 =} UW² + VW² – 2(UW)(VW) cos U

UV2² = 15² + 12² – 2(15)(12) cos 50^o

UV [Tex]\sim[/Tex]9.83cm

Question 8: Construct a triangle KLM, KL = 10cm. LM = 6cm and angle L = 75^o

Solution:

Triangle KLM

Draw a line segment KL = 10cm

At point K, draw angle L = 75^o

By using the Law of Cosines to find the length of side KM:

KM² = KL² + LM² – 2(KL)(LM) cos L

KM² = 10² + 6² – 2(10)(6) cos 75^o

KM [Tex]\sim[/Tex] 8.48cm

Question 9: Construct a triangle whose two angle measurements are 40^o and 70^o and the side length between them is 8cm.

Solution:

Triangle ACB

Draw the line of length 8cm using a ruler AC = 8cm

Put the center of the protractor on point A and measure 40^o.

Now, put the construction mark at 40^o

Using the ruler, draw a long line from A through the construction mark.

Again, place the center of the protractor on point B and measure 70^o

Now, put a mark on 70^o and more the intersection point as C.

Now, draw a line by joining points B and C.

Hence, △ABC is constructed.

Question 10: Construct a triangle ABC whose side lengths are 3cm, 5cm, and 6cm.

Solution:

Triangle ABC

Draw the longest side using ruler AB = 6cm.

Take a compass, and draw an arc above line AB from point A, whose measurement is 5cm.

Similarly from point B, draw an arc whose measurement is 3cm.

Mark the intersection point as C and join CA and CB using a ruler.

Hence, △ABC is constructed.

In this article, we are going to see solved questions and also practice questions for a better understanding of the concept of the construction of triangles.