Given triangle ABC with incenterI, suppose that the three triangles ABI, BCI, and ACI all have equal area. Prove that triangle ABC is equilateral. 1.Given AABC with incenter I, suppose that the three triangles AABI, ABCI, andAACI all have equal area. Prove that AABC is equilateral.

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Answered: 1. Given AABC with incenter I, suppose…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Given triangle ABC with incenterI, suppose that the three triangles ABI, BCI, and ACI all have equal area. Prove that triangle ABC is equilateral.

1.
Given AABC with incenter I, suppose that the three triangles AABI, ABCI, and
AACI all have equal area. Prove that AABC is equilateral.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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