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Circle D circumscribes ABC and ABE. Which statements about the triangles are true?


Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE.
Statement II: The distance from C to D is the same as the distance from D to E.
Statement III: bisects CDE.
Statement IV: The angle bisectors of ABC intersect at the same point as those of ABE.



I only
I and II
II and IV
I and III
III and IV

Respuesta :

Answer:

I and II

Step-by-step explanation:

Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE.

Statement 1 is true because the perpendicular bisectors intersect at the center of the circumcircle.

Since the two triangles have the same circumcircle, therefore, their perpendicular bisectors intersect at the same point. So statement I is true.

Statement II: The distance from C to D is the same as the distance from D to E.

Since they both, that is distance from C to D and the distance from D to E represent the radius of the circle therefore, they both are equal in length.

Therefore, only I and II are correct.

Based on the information about the triangles, the true statements include:

  • Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE.
  • Statement II: The distance from C to D is the same as the distance from D to E.

Triangles

It should be noted that Statement 1 is true because the perpendicular bisectors intersect at the center of the circumcircle.

Also, since the two triangles have the same circumcircle, the perpendicular bisectors intersect at the same point.

Therefore, the correct options are I and II.

Learn more about triangles on:

https://brainly.com/question/24382052

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