4.6.26. Consider a regular triangular board of side length 2". The board consists of 4" equilateral triangle of side length 1. Show that, if one of the corner triangles is removed, then the remaining board can be tiled by isosceles trapezoids (as in the diagram), each covering exactly three triangles.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 90E
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4.6.26. Consider a regular triangular board of side length 2". The board consists of 4" equilateral triangles
of side length 1. Show that, if one of the corner triangles is removed, then the remaining board can be
tiled by isosceles trapezoids (as in the diagram), each covering exactly three triangles.
Transcribed Image Text:4.6.26. Consider a regular triangular board of side length 2". The board consists of 4" equilateral triangles of side length 1. Show that, if one of the corner triangles is removed, then the remaining board can be tiled by isosceles trapezoids (as in the diagram), each covering exactly three triangles.
Read carefully exercise 4.6.26 on p. 103. Assume that we want to prove this statement by strong induction.
How should we position the green trapezoid to apply the induction assumption in the proof of the inductive
step? Enter below the number of the correct picture. Notice that blue lines represent medians of the triangle.
Pic 1
Pic 2
2"
Pic 3
Transcribed Image Text:Read carefully exercise 4.6.26 on p. 103. Assume that we want to prove this statement by strong induction. How should we position the green trapezoid to apply the induction assumption in the proof of the inductive step? Enter below the number of the correct picture. Notice that blue lines represent medians of the triangle. Pic 1 Pic 2 2" Pic 3
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