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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

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

In Exercises 39 and 42, refer to the line segments shown.

Use the following theorem to construct a triangle similar to the given triangle but with sides that are twice the length of those of the given triangle.

Theorem: If the lengths of the three pairs of sides for two triangles are in proportion, then those triangles are similar (SSS˜).

To determine

To construct:

The triangle similar to the given triangle but with sides that are twice the length of those of the given triangle.

Explanation

Theorem:

If the lengths of the three pairs of sides for two triangles are in proportion, then those triangles are similar.

Calculation:

Construct the given triangle ABC as shown in figure.

To construct a triangle similar to ABC but twice the size, follow the below procedure:

1. Take any arbitrary point Y and draw a horizontal line XZ equal to twice the length of BC.

2. Take Y as center and draw an arc equal to twice the length of AB above the line YZ and take Z as center and draw an arc equal to twice the length of AC above the line YZ to obtain the intersection point X.

3. Draw the lines XY and XZ to obtain the triangle twice the size of the triangle ABC as shown below:

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