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 all the three sides are given.
Before we start constructing the triangle, we have to check the following important property of triangle is met by the lengths of all the three sides.
"The sum of any two sides of a triangle is always greater than the third side"
If the above mentioned property of triangle is not met by the given three sides, we will not be able to construct a triangle with those three sides.
To construct a triangle when the lengths of all the three sides are given, we must need the following mathematical instruments.
1. Ruler
2. Compass
The steps for the construction of a triangle when the lengths of all the three sides are given.
Example :
Construct a triangle ABC given that AB = 4cm, BC = 6 cm and AC = 5 cm.
Given measurements :
AB = 4cm
BC = 6 cm
AC = 5 cm
Step 1 :
Draw a line segment BC = 6cm
(Here we take the longest side)
Step 2 :
With ‘B’ as centre, draw an arc of radius 4 cm above the line BC.
Step 3 :
With ‘C’ as center, draw an arc of 5 cm to intersect the previous arc at ‘A’
Step 4 :
Join AB and AC.
Now ABC is the required triangle.
This construction clearly shows how to construct a triangle when the lengths of all the three sides are given with compass and straightedge or ruler.
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.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
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 fractions
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
©All rights reserved. onlinemath4all.com
May 23, 22 01:59 AM
Exponential vs Linear Growth Worksheet
May 23, 22 01:59 AM
Linear vs Exponential Growth - Concept - Examples
May 23, 22 01:34 AM
SAT Math Questions on Exponential vs Linear Growth