PROPERTIES OF TRIANGLE
About "Properties of Triangle"
Properties of Triangle :
The following are the two important properties of triangle.
1. The sum of the lengths of any two sides of a triangle is greater than the third side.
2. The sum of all the three angles of a triangle is 180°.
Some other properties of triangle
1. In an equilateral triangle, all the three sides and three angles will be equal and each angle will measure 60°.
2. In an isosceles triangle, the lengths of two of the sides will be equal. And the corresponding angles of the equal sides will be equal.
2. In a right triangle, square of the hypotenuse is equal to the sum of the squares of other two sides. This is known as Pythagorean theorem.
Hypotenuse :
The longest side of in the right triangle which is opposite to right angle (90°)
Properties of Triangle - Problems
Problem 1 :
Is it possible to have a triangle whose sides are 5 cm, 6 cm and 4 cm ?
Solution :
According to the properties of triangle explained above, if the sum of the lengths of any two sides is greater than the third side, then the given sides will form a triangle.
Let us apply this property for the given sides.
5 cm + 6 cm > 4 cm.
6 cm + 4 cm > 5 cm.
5 cm + 4 cm > 6 cm
Since the given sides meet the condition said in the property, It is possible to have a triangle whose sides are 5 cm, 6 cm and 4 cm.
Problem 2 :
Is it possible to have a triangle whose sides are 7 cm, 2 cm and 4 cm ?
Solution :
According to the properties of triangle explained above, if the sum of the lengths of any two sides is greater than the third side, then the given sides will form a triangle.
Let us apply this property for the given sides.
2 cm + 4 cm < 7 cm.
From the above point, it is clear the sum of the lengths of the two sides 2 cm and 4 cm is less than the third side 7 cm.
The given sides do not meet the condition said in the property.
Hence, it is not possible to have a triangle whose sides are 7 cm, 2 cm and 4 cm.
Problem 3 :
Find the length of the hypotenuse of the right triangle where the lengths of the other two sides are 8 units and 6 units.
Solution :
From the given information we can draw the triangle as given below.
In the above triangle, we have to find the value of "x"
According to Pythagorean theorem, square of the hypotenuse is equal to the sum of the squares of other two sides
So, we have
x² = 8² + 6²
x² = 64 + 36
x² = 100
x = 10
Hence, the length of the hypotenuse is 10 units.
Problem 4 :
The hypotenuse of a right angled triangle is 20 cm. The difference between its other two sides is 4 cm. Find the length of the sides.
Solution :
Let "x" and "x+4" be the lengths of other two sides.
Using Pythagorean theorem, (x+4)² + x² = 202
x² + 8x + 16 + x² - 400 = 0
2x² + 8x - 384 = 0
x² + 4x - 192 = 0
(x+16)(x-12) = 0
x = -16 or x = 12
x = -16 can not be accepted. Because length can not be negative.
If x = 12,
x + 4 = 12 + 4 = 16
Hence, the other two sides of the triangle are 12 cm and 16 cm.
Apart from the problems given above, if you need more problems on triangle properties, please click the following links.
After having gone through the stuff given above, we hope that the students would have understood "Triangle properties".
Apart from the stuff given above, if you want to know more about "Triangle properties", please click here
If you need any other stuff in math, please use our google custom search here.
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
