Triangle Trisectors

Geometry Level 3

The measures of the angles of $\triangle ABC$ have a ratio of $1:2:3$ . Each angle of $\triangle ABC$ is trisected, and the three nearest points of intersection of the adjacent angle trisectors are used to form a new triangle $\triangle DEF$ . What is the ratio of the measures of the angles of $\triangle DEF$ ?

1:1:1

1:1:2

1:\sqrt{3}:2

1:\sqrt{2}:\sqrt{2}

1:2:3

1 solution

David Vreken
Jan 9, 2018

Morley’s Trisector Theorem states that the three points of intersection of adjacent angle trisectors form an equilateral triangle. Therefore, $\triangle DEF$ is an equilateral triangle, and the ratio of the measures of the angles is $1:1:1$ .

Triangle Trisectors

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