The triangle with vertices (0, 0), (2, 1), and (0, 5) can be cut into pieces that are eachcongruent to the triangle with vertices (2, 0), (3,0), and (3, 2). Show how.

Answered: The triangle with vertices congruent to…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.1: Rectangular Coordinate Systems

Problem 15E

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Question

The triangle with vertices (0, 0), (2, 1), and (0, 5) can be cut into pieces that are each
congruent to the triangle with vertices (2, 0), (3,0), and (3, 2). Show how.

Expert Solution

Step 1

The vertices of triangle are A(0, 0), B(2,1) and C(0,5).

The vertices of other triangle are P(2, 0), Q(3,0) and R(3,2).

Let find the distance between the vertices using the distance formula for the triangle ABC.

$A B = \sqrt{{(2 - 0)}^{2} + {(1 - 0)}^{2}} = \sqrt{5}$

$B C = \sqrt{{(5 - 1)}^{2} + {(0 - 2)}^{2}} = \sqrt{20} = 2 \sqrt{5}$

$A C = \sqrt{{(5 - 0)}^{2} + {(0 - 0)}^{2}} = 5$

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The triangle with vertices congruent to the triangle