__Construct a triangle when two sides and an included angle are 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 the lengths of two sides and the angle included are given.

To construct a triangle when the lengths of two sides and the angle included are given, we must need the following mathematical instruments.

1. Ruler

2. Compass

3. Protractor

The steps for the construction of a triangle, when the lengths of two sides and the angle included are given

Construct a triangle PQR given that PQ = 4 cm, QR = 6.5 cm and <PQR = 60°.

Given measurements :

PQ = 4 cm

QR = 6.5 cm

<PQR = 60°

Step 1 :

Draw the line segment QR = 6.5 cm.

(Here we take the longest side)

Step 2 :

Using protractor, at Q, draw a line QX making an angle of 60° with QR.

Step 3 :

With Q as centre, draw an arc of radius 4 cm to cut the line (QX) at P.

Step 4 :

Join PR.

Now, PQR is the required triangle.

This construction clearly shows how to construct a triangle with the mathematical instruments compass, ruler and protractor when two sides and an included angle 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 = 2cm, QR = 6cm, 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 = 4cm

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 "Construct a triangle when two sides and an included angle are given"

If you want to know more about "Construct a triangle when two sides and an included angle are given", please click here

If you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**