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H is the circumcenter, or point of concurrency, of the perpendicular bisectors of ΔACE.
Triangle A C E is shown. Point H is the circumcenter of the triangle. Lines are drawn from each point of the triangle to point H. Lines are drawn from point H to the sides of the triangle to form right angles. Line segments H B, H F, and H D are formed.
Which statements must be true regarding the diagram?

Respuesta :

natrtab1

Answer:

∠HDC ≅ ∠HDE, AB ≅ BC, HC ≅ HE

Step-by-step explanation:

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The circumcenter describes the point of intersection of three perpendicular bisectors. Any point on the perpendicular bisector is equidistant from the endpoint of the segment. Hence, the true statements are :

  • HC ≈ HE
  • ∠HDC ≈ ∠HDE
  • AB = BC

The intersection point H is equidistant from the vertices of the triangle A, C and E

Therefore, HA ≈ HC ≈ HE ; Hence, the expression ;

  • HC ≈ HE

B is the midpoint of the line AC ; Hence, using the midpoint rule ; AB = BC

  • ∠HDC ≈ ∠HDE

Therefore, only the three statements are true.

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