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 C
F ⊥ 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.
2 answers:
BE, CF and AG are angle bisectors. Therefore, their meeting point is I, the incentre of the triangle ABC.
BE ⊥ AC, AG ⊥ BC, and CF ⊥ AB. Therefore, meeting point of BE, CF and AG is O, the orthocentre of the triangle ABC.
BE bisects AC, CF bisects AB, and AG bisects BC. Therefore, BE, CF and AG are medians and their meeting point is G, the centroid of the triangle ABC.
From the above, it is clear that I = O = G.
This property holds good only for equilateral triangles.
Hence, Δ ABC is an equilateral triangle.
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Answer:
The inequality that represents the age of the group, "x", is:
Step-by-step explanation:
To express this problem in an inequality we will attribute the age of the members on the group with the variable "x". There are two available information about "x", the first states that every member of the group is older than 17 years, therefore we can create a inequality based on that:
While the second data from the problem states that none of than is older than 54 years old, this implies that they can be at most that old, therefore the inequality that represents this is:
In order for both to be valid at the same time x must be greater than 17 and less or equal to 54, therefore we finally have: