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If the length of three of the altitudes of a triangle are equal, then the triangle must be a/an
- a)Isosceles triangle
- b)Equilateral triangle
- c)Scalene triangle
- d)Right triangle
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If the length of three of the altitudes of a triangle are equal, then ...
In Δs BEC and CFB
BC = BC (Common)
BE = CF (Given)
∠BEC = ∠CFB = 90°
∴ ΔBEC = ∠CFB = 90°
(By R-H-S congruence criterion)
∠B =∠C (C-P-C-T)
∴ AB = AC ...(i)
Similarly in Δs ADC and C + A
⇒ ∠A = ∠C
∴ AB = BC ...(ii)
Using (i) and (ii)
AB = BC = AC (Δ should be equilateral)
BC = BC (Common)
BE = CF (Given)
∠BEC = ∠CFB = 90°
∴ ΔBEC = ∠CFB = 90°
(By R-H-S congruence criterion)
∠B =∠C (C-P-C-T)
∴ AB = AC ...(i)
Similarly in Δs ADC and C + A
⇒ ∠A = ∠C
∴ AB = BC ...(ii)
Using (i) and (ii)
AB = BC = AC (Δ should be equilateral)
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