2016 · Q88
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?
- 1XYZ is an equilateral triangle.
- 2Triangle XYZ is similar to triangle ABC.
Select the correct answer using the code given below.
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
With BX = CY = AZ and 60° vertex angles, SAS gives XZ = YX = ZY. Thus XYZ is equilateral, so statement 1 is true. All equilateral triangles are similar, so statement 2 is true. Hence both, option C.