How to Construct a Triangle When Two Angles and One Side is Given :
The way of constructing a triangle is depending on the information given.
Here we are going to see, how to construct a triangle when two angles and one side is given.
To construct a triangle when two angles and one side is given, we must need the following mathematical instruments.
1. Ruler
2. Protractor
Construct a triangle XYZ given that XY = 6 cm, ∠ZXY = 30° and <XYZ = 100°. Examine whether the third angle.
Given measurements :
XY = 6 cm
∠ZXY = 30°
∠XYZ = 100°
Step 1 :
Draw the line segment XY = 6cm.
Step 2 :
Using protractor, at X, draw a ray XP making an angle of 30° with XY.
Step 3 :
Using protractor, at Y, draw another ray YQ making an angle of 100° with XY. The rays XP and YQ intersect at Z.
Step 4 :
Using the property, "Sum of the three angles of any triangle is 180°", we can find the third angle which is 50°. That is, ∠Z = 50°.
Now, XYZ is the required triangle.
This construction clearly shows how to construct a triangle with the mathematical instruments ruler and protractor when two angles and one side are given.
If lengths of all the three sides are given, can always we construct a triangle ?
Let us get answer for the above question with an example.
A student attempted to draw a triangle with given measurements PQ = 2 cm, QR = 6 cm, PR = 3 cm. First he drew QR = 6cm. Then he drew an arc of 2cm with Q as centre and he drew another arc of radius 3 cm with R as centre. They could not intersect each to get P.
What is the reason ?
Given measurements :
PQ = 2 cm
QR = 6 cm
PR = 3 cm
Step 1 :
Draw a line segment QR = 6cm
(Here we take the longest side)
Step 2 :
With ‘R’ as centre, draw an arc of radius 3 cm above the line QR.
Step 3 :
With ‘Q’ as center, draw an arc of c cm above the line QR
Step 4 :
Now, the arc said in step 2 and arc said in step 3 must intersect.
Let us apply the above steps and see whether the two arcs intersect.
In the above figure, the two arcs said in step 2 and step 3 do not intersect.
Since the two arcs do not intersect, we can not draw a triangle with the given the three sides.
Reason :
According to the property of triangles, we have that he sum of any two sides of a triangle is always greater than the third side.
But here, the sum of the two sides 2 and 3 is less than the third side 6.
After having gone through the stuff given above, we hope that the students would have understood how to construct a triangle when two angles and one side is given.
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