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ABC is an equilateral triangle and X, Y and Z are the points on BC, CA and AB respectively such that BX = CY = AZ. Which of the following is/are correct?
1. XYZ is an equilateral triangle.
2. Triangle XYZ is similar to triangle ABC
Select the correct answer using the code given below.
  • a)
    1 only
  • b)
    2 only
  • c)
    Both 1 and 2
  • d)
    Neither 1 nor 2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
ABC is an equilateral triangle and X, Y and Z are the points on BC, CA...
Let the side of triangle ABC be a
Let BX = CY = AZ = t
⇒ XC = AY = ZB = a – t
In triangle BXZ and CYX
BX = CY [Given]
⇒ BZ = XC = a – t
∠B = ∠C = 60°              [Equilateral triangle]
⇒ BXZ ≅ CYZ               [∵ SAS ≅]
⇒ XZ = XY
Following same algorithm
⇒ ZY = XY
⇒ XYZ is an equilateral triangle
⇒ Statement I is true
All equilateral triangles are similar to each other
⇒ Statement II is true
∴ Both statement I and II are true.
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Most Upvoted Answer
ABC is an equilateral triangle and X, Y and Z are the points on BC, CA...
Explanation:

Given, ABC is an equilateral triangle and BX = CY = AZ, which means the points X, Y, and Z are equidistant from the sides of triangle ABC.

1. XYZ is an equilateral triangle:
Since BX = CY = AZ, the triangle XYZ is also equilateral, as each side is equal to BX = CY = AZ.

2. Triangle XYZ is similar to triangle ABC:
Since XYZ is equilateral, all its angles are equal to 60°. Also, since BX = CY = AZ, the angles BXC, CYA, and AZB are equal, which means that the angles of triangle ABC opposite to these sides are also equal. Therefore, triangle XYZ is similar to triangle ABC.

Hence, both statements 1 and 2 are correct. Therefore, the correct answer is option C.
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ABC is an equilateral triangle and X, Y and Z are the points on BC, CA and AB respectively such that BX = CY = AZ. Which of the following is/are correct?1. XYZ is an equilateral triangle.2. Triangle XYZ is similar to triangle ABCSelect the correct answer using the code given below.a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer?
Question Description
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