   Chapter 5.3, Problem 10E 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

In Exercises 9 to 12, name the method that explains why ∆ D G H ~ ∆ D E F . D E = 3 · D G and D F = 3 · D H To determine

To name:

The method that explains why DGH~DEF

Explanation

Given:

The triangle,

Here,

DE=3·DG and DF=3·DH

Approach:

Two polygons are similar if and only if two conditions are satisfied.

1. All pairs of corresponding angles are congruent.

2. All pairs of corresponding sides are proportional.

Definitions:

AA:

If the two angles of one triangle are congruent to the two angles of a another triangle, then the triangles are similar.

SAS:

If an angle of one triangle is congruent to an angle of a second triangle and the pairs of sides including the angles are proportional (in length), then the triangles are similar.

SSS:

If the three sides of one triangle are proportional (in length) to the three corresponding sides of a second triangle, then the triangles are similar.

Description:

For the given triangle,

It is given that,

DE=3·DG and DF=3·DH

There are two triangles DGH and DEF

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