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Home >> Triangle >> Properties >> Pythagoras Theorem >> Examples

Define Pythagoras Theorem : Solved Examples

Sum of Two Sides Angle Sum Property Angles opposite to equal sides of triangle are equal Angle opposite to longer side is greater Pythagoras Theorem
Exterior Angle Property of a Triangle Mid point property of Triangle Triangles on same base & between same parallel lines

In the following diagram, AB = AD = 5 cm, AC = 4 cm, find BD.

With-in the given △ ABD there are two other triangles:
△ ABC
△ ACD

And BD = BC + CD……………(Statement 1)

In △ ABC:
AB = hypotenuse = 5 cm
AC = side 1 = 4 cm
BC = ??
Apply Pythagoras Theorem and we get:
(Hypotenuse)2 = (side 1)2 + (side 2)2

Or we can also write it as:
(AB)2 = (AC)2 + (BC)2

Put the values of Side 1 and hypotenuse from above and we get
(5)2 = (4)2 + (BC)2

Find square of 5 & 4 and we get:
25 = 16 + (BC)2

Subtract 16 from both sides and we get:
9 = (BC)2

Take square root of both sides and we get:
3 = BC

Or we can write as:
BC = 3 cm

Similarly, in △ ACD, we will find CD and we get:
CD = 3 cm

Now, put the values of BC and CD in statement 1 & we get:
BD = BC + CD
= 3 + 3
= 6

Hence, BD = 6 cm

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