Construction of Triangles

Introduction to construction of triangles:

The triangles can be constructed if the following requirements are given such as follows,

The measurement of three sides should be given (or)

The measurement of the two sides and the included angle should be given (or)

The measurement of a side and any two angles should be given.

Now we are going to see about the construction of triangles. Is this topic Scalene Triangles hard for you? Watch out for my coming posts.


Construction of triangles:


Construction of triangles if three sides are given:

Construct a triangle if three sides are given with x, y and z measurements.

Steps of construction:

First a line segment QR of x cm length should be drawn.

With Q as center and radius of y cm be drawn and it equals to PQ and draw an arc of a circle.

With R as center and radius of PR = z cm and draw an arc and it will intersects at the first arc of point P.

Now join the points of line segments PQ and PR.

Thus, PQR is a required triangle. I have recently faced lot of problem while learning Geometry Definition, But thank to online resources of math which helped me to learn myself easily on net.

Other constructions of triangles:

Construction of triangles if two sides and angle are given:

Construct a triangle if two sides and an angle are given.

Steps of Construction:

First we have to draw a ray of QX of some length.

With the help of protractor measure the given angle and draw the line to meet Q.

The ray QY which may cut line segment QR of x cm.

The ray QY which may cut the line segment QP of y cm.

Now we can join the two points P and R.

Thus, PQR is the required triangle.

Construction of triangles if two angles and Side are given:

Construct a triangle if two angles and a side are given.


Steps of Construction:

First we should draw the line segment of QR of given length.

With the help of the protractor measure the given angle at RQX

Then, draw QRY for the given angle such that XY lie on the same side of the PQ.

Then, label the point where it intersects at QX and QY as P.

Thus, the PQR is the required triangle.

Measuring Irregular Triangles

Introduction for measuring irregular triangles:

The irregular triangle is nothing but the triangle where the three sides are not equal and the angles present in it also different during its measurement. The only irregular triangle is the scalene triangle. Now we are going to see about the measuring of irregular triangle with some example problems.


About Measuring of Irregular Triangle:
Now we are going to see about the irregular triangles and its measurement. The irregular triangle is nothing but the scalene triangle where the sides are unequal in its length and the angles in it also unequal.

When the two sides and an angle are given and if we want to find the third side of an irregular triangle, then use the formula which is given below,

c2 = a2 + b2 - 2ac * cos ?

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Problems for Measuring Irregular Triangle:

Example 1:

The sides of the triangle are 5cm and 10 cm and the angle measuring is 40. Determine the third side of the irregular triangle.

Solution:

The third side of the triangle can be calculated by using the formula,

c2 = a2 + b2 - 2ac * cos ?

Now substitute the values in the formula we get,

c2 = 52 + 102  2(5)(10) * cos 40

Now square the values which are substituted in the formula as follows,

= 25 + 100  100 cos 40

c2 = 48.39

c = `sqrt 48.39`

c = 6.95

The value can be rounded as 7cm.

Example 2:

Find the third side of the triangle whose measurements of the triangle are 7cm, 8cm and angle measuring is about 50 degree.

Solution:

The third side of the triangle can be calculated by using the formula,

c2 = a2 + b2 - 2ac * cos ?

Now substitute the values in the formula we get,

c2 = 72 + 82  2(7)(8) * cos 40

= 49 + 64  112 cos 50

c2 = 41

c = ` sqrt 41`

c = 6.4

The value can be rounded as 6cm.