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

Examples of repetition need not be boring- learning maths, E1) Try and see ...

E1) Try and see the order in which different children fills numbers in the grid above. My claim is that all of them would fill in the ones, the fives and the tens first. Test my hy

Linda bought 35 yards of fencing how much did she spend, Linda bought 35 ya...

Linda bought 35 yards of fencing at $4.88 a yard. How much did she spend? To multiply decimals, multiply generally, count the number of decimal places in the problem, then us

Describe about parallel and perpendicular lines, Describe about Parallel an...

Describe about Parallel and Perpendicular Lines ? Parallel Lines : Parallel lines are coplanar lines (lines that lie in the same plane) that never intersect. The bl

Assignment, Is there any assignment work available for mathematics?

Is there any assignment work available for mathematics?

Developing pre-number concepts, DEVELOPING PRE-NUMBER CONCEPTS :  Previous...

DEVELOPING PRE-NUMBER CONCEPTS :  Previously you have read how children acquire concepts. You know that, for children to grasp a concept, they must be given several opportunities

Rounding decimals, i need help rounding decimals to the nearest 100th and t...

i need help rounding decimals to the nearest 100th and tenth

Marketing mix, 1) Identify key characteristics of product or services and e...

1) Identify key characteristics of product or services and estimate their significance to the market 2) Identify and analyse level of customer service provision to determine its si

Drug administration, A drug is administrated once every four hours. Let D(n...

A drug is administrated once every four hours. Let D(n) be the amount of the drug in the blood system at the nth interval. The body eliminates a certain fraction p of the drug duri

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