If the altitudes of a triangle ABC are equal,then prove that triangle is equilateral.

 

Given, AD, BE and CF are the attitudes drawn on sides BC, CA and AB of Δ ABC such that AD = BE = CF

Area of Δ ABC = × BC × AD =  × AB × CF =  × CA × BE (Area of Δ =  × Base × Correspondence attitude)

∴ BC × AD = AB × CF = CA × BE

⇒ BC = AB = CA ( AD = BE = CF)

Hence, ΔABC is an equilateral triangle.

  • 60

Prove tht the bisectors of the angles of a linear pair are right angles

  • -1

prove tht the measure of each angle of an equalateral triangle is 60

solve this one nt the above one plzzz i got  tht

  • -3

Steps

Statement

Reason

 

 

 

 

1

Consider triangles BEC and BFC

2

EC=BF

Equal altitudes(given)

3

 BEC=BFC = 900

BE and BF are Altitudes

4

BC is common

 

5

BEC BFC

RHS postulate

6

ABC = BCA

Corresponding angles

7

Consider the ADB and ADC

8

 ADB=ADC = 900

AD is Altitude

9

AD is common

 

10

ABC = BCA

Step 6

11

ADB ADC

ASA postulate

12

AB =AC

Corresponding sides are equal

13

BC= AC

Similarly we can prove BFC BFA

14

AB=AC=BC

Step 12,13

 

  • 11
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