Question

in a triangle product of all three sides with their respective altitudes are equal to each other.
True or false


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Answer 1

Answer:

true

Step-by-step explanation:

For any point P within an equilateral triangle, the sum of the perpendiculars to the three sides is equal to the altitude of the triangle. This is Viviani's theorem.

Answer 2

Step-by-step explanation:

In △ABC,

BD⊥AC and CE⊥AB

In △BDC and △CEB

⇒ ∠BDC=∠CEB [ Each 90

o

]

⇒ ∠DCB=∠EBC [ Angles opposite equal sides are equal ]

⇒ BC=CB [ Common side ]

∴ △BDC≅△CEB [ AAS rule ]

⇒ BD=CE [ By C.P.C.T. ]

∴ The given statement is false.