   Chapter 8.1, Problem 1E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Suppose that two triangles have equal areas. Are the triangles congruent? Why or why not? Are two squares with equal areas necessarily congruent? Why or why not?

To determine

Whether two triangles with equal areas are congruent or not and two squares with equal areas are necessarily congruent or not

Explanation

Given,

Consider the two triangles having equal areas.

Let the first triangle is ΔABC and the second triangle is ΔDEF.

The first triangle (ΔABC):

Let b=x and h=x2

Area of the triangle

A=12bh

=12xx2

=x24

The second triangle (ΔDEF):

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