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In the diagram, which must be true for point D to be an orthocenter?

BE, CF, and AG are angle bisectors.
BE ⊥ AC, AG ⊥ BC, and CF ⊥ AB.
BE bisects AC, CF bisects AB, and AG bisects BC.
BE is a perpendicular bisector of AC, CF is a perpendicular bisector of AB, and AG is a perpendicular bisector of BC.


Please help!!!

In the diagram which must be true for point D to be an orthocenter BE CF and AG are angle bisectors BE AC AG BC and CF AB BE bisects AC CF bisects AB and AG bi class=

Respuesta :

merlynthewhizz
A copy of the diagram is shown below

Point D is the intersection of three angle bisector. 
BE is the angle bisector of ∠B
CF is the angle bisector of ∠C
AG is the angle bisector of ∠A

Point D is also the intersection between three perpendicular bisector
BE is the perpendicular bisector of AC
AG is the perpendicular bisector of BC
CF is the perpendicular bisector of AB

Hence the correct statements is statement 1 and statement 4


Ver imagen merlynthewhizz

A true statement for point D to be an orthocenter is given by BE ⊥ AC,

AG ⊥ BC, and CF ⊥ AB.

What is an orthocenter?

" An orthocenter is defined as the intersecting point of all the altitudes of a triangle passing through a vertex and intersecting on the opposite side of it."

According to the question,

  • BE, CF, and AG are angle bisectors, the point of concurrency of the angle bisector is known as the incenter.

     

         This is not the correct answer.

  • BE ⊥ AC, AG ⊥ BC, and CF ⊥ AB,  the point of concurrency of the altitudes is known as the orthocenter.

             

       This is the correct answer.

  • BE bisects AC, CF bisects AB, and AG bisects BC, point of concurrency of all the medians is known as the centroid.

       This is not the correct answer.

  • BE is a perpendicular bisector of AC, CF is a perpendicular bisector of AB, and AG is a perpendicular bisector of BC, point of concurrency of perpendicular bisector is known as circumcenter.

        This is not the correct answer.

Hence, a true statement for point D to be an orthocenter is given by

BE ⊥ AC, AG ⊥ BC, and CF ⊥ AB.

Learn more about orthocenter here

https://brainly.com/question/19763099

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