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In an equilateral triangle ABC, a line segment is drawn from each vertex to a point on the opposite side so that the segment divides the side in the ratio 1:2, creating another equilateral triangle DEF (see below). 0 F

In an equilateral triangle ABC, a line segment is drawn from each vertex to a point on the opposite side so that the segment divides the side in the ratio 1:2, creating another equilateral triangle DEF (see below). 0 F

Elementary Geometry For College Students, 7e
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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In an equilateral triangle ABC, a line segment is drawn from each vertex to a point on the opposite side so that the segment divides the side in the ratio 1:2, creating another equilateral triangle DEF (see below). A E B D (a) What is the ratio of the areas of the two equilateral triangles? To answer this question, (i) create the above diagram with your geometry package. (ii) measure the lengths of the sides of the two equilateral triangles. (iii) find the areas of the two equilateral triangles and the ratio between them. (b) Repeat the procedure above for at least two other side ratios, 1:n.
Transcribed Image Text:In an equilateral triangle ABC, a line segment is drawn from each vertex to a point on the opposite side so that the segment divides the side in the ratio 1:2, creating another equilateral triangle DEF (see below). A E B D (a) What is the ratio of the areas of the two equilateral triangles? To answer this question, (i) create the above diagram with your geometry package. (ii) measure the lengths of the sides of the two equilateral triangles. (iii) find the areas of the two equilateral triangles and the ratio between them. (b) Repeat the procedure above for at least two other side ratios, 1:n.
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