Prove sum of squares any two sides equal twice square, Mathematics

Assignment Help:

Prove that in any triangle the sum of the squares of any two sides is equal to twice the square of half of the third side together with twice the square of the median, which bisects the third side.

Ans:    To prove AB2 + AC2 = 2AD2 + 2 (1/2 BC)2

Draw AE ⊥ BC

2080_triangle the sum of the squares.png

In Δ ABD since ∠D > 900

∴AB2 = AD2 + BD2 + 2BD x DE ....(1)

Δ ACD  since ∠ D < 90o

AC2 = AD2 + DC2 - 2DC x DE   ....(2)

Adding (1) & (2)

AB2 + AC2 = 2(AD2 + BD2)

= 2(AD2 + ( 1/2 BC )2)

Or AB2 + AC2 = 2 (AD2 + BD2)

Hence proved


Related Discussions:- Prove sum of squares any two sides equal twice square

Mensuration, A palm tree of heights 25m is broken by storm in such a way th...

A palm tree of heights 25m is broken by storm in such a way that its top touches the ground at a distance of 5m from its root,but is not separated from the tree.Find the height at

Unbounded intervals, Intervals which extend indefinitely in both the ...

Intervals which extend indefinitely in both the directions are known as unbounded intervals. These are written with the aid of symbols +∞  and -  ∞  . The various types

What is angles, What is Angles? An angle is made up of two rays with a ...

What is Angles? An angle is made up of two rays with a common endpoint, which is called the vertex. The sides of the angle are rays. An angle is denoted by "θ". When two li

Definition of functions, Definition: An equation is considered as function...

Definition: An equation is considered as function if for any x in the domain of the equation (the domain is the entire x's which can be plugged into the equation) the equation wil

How many dollars did they raise the first two days, The freshman class is p...

The freshman class is participating in a fundraiser. Their target is to raise $5,000. After the first two days of the fundraiser, they have raised 32 percent of their goal. How man

50+50, what is the totel

what is the totel

Objective type , when is the trnscribing process of data preparation irrele...

when is the trnscribing process of data preparation irrelevant ? a)CAPI b) mall panel c) in home interview d) all of them

Differentiate the equation x = x (t ) and y = y (t ) , Suppose that x = x (...

Suppose that x = x (t ) and y = y (t ) and differentiate the following equation with respect to t. Solution                                         x 3 y 6 + e 1- x - cos (5

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd