Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

Prove that the altitudes of a triangle are concurrent.

Prove that the altitudes of a triangle are concurrent.

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
240-423_plot-formula.jpg
We need to prove that altitudesAD,BEandCFintersect
at one point.Let us draw the straight lineGHpassing throughthe pointCparallel to the triangle sideAB.
Similarly, we can construct lineGIpassingthrough the pointBparallel to sideAC, andthe straight lineHIpassing through the pointAparallelto the triangle sideBC. LetG,H, andIbe the intersection points of the constructed straight lines.
Now, quadrilateralABCHhas the opposite sides parallel, therefore its opposite sides are of equal length in accordance to the properties of sides of parallelograms
In particular, the sidesABandHCare of equal length:AB=HC.
Similarly, the sidesABandCGare of equal length:AB=CG(from the quadrilateralABGC). Hence,HC=CG, and the pointCis the midpoint of the segmentHG.
By the same reason, the pointAis the midpoint of the segmentHI(BC=AHfrom the quadrilateralBCHA, andBC=AIfrom the quadrilateralBCAI, which givesAH=AI).
Finally, the pointBis the midpoint of the segmentGI(AC=BGfrom the quadrilateralBGCA, andAC=BIfrom the quadrilateralIBCA, which givesBG=BI).
Thus the pointsA,BandCare the midpoints of the sides of the triangleIGH, and the altitudesAD,BEandCFof the original triangleABCare the perpendiculars to the sides of the constructed triangleIGHat the midpoints of its sides. Therefore, the segmentsAD,BEandCFintersect in one common point
Thanks and Regards
Shaik Aasif
askIITians faculty

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free