2. Construct pentagons on the sides of the right triangle. Use the regular polygon tool to construct a pentagon (5-sided figure) on each side of the right triangle. (Be careful about the order in which you select the first two vertices of the regular polygon. Select them in the order that makes the pentagon appear on the outside of the right triangle.) 3. Conjecture a relationship between the pentagon areas. Use the area measuring tool and click on the three pentagons to display their areas. Take a screenshot and write a caption describing the relationship between the areas of the three pentagons.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter4: Quadrilaterals
Section4.3: The Rectangle, Square, And Rhombus
Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...
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number 2 and 3 

Thales' Theorem
is the diameter of a
If AB
circle centered at O and c
is any other
then the angle ZACB is right.
point
on the circle,
B
A
Proof outline:
1. Let AB be the diameter of a circle centered at o
and let C be
any
other point on the circle.
A
Transcribed Image Text:Thales' Theorem is the diameter of a If AB circle centered at O and c is any other then the angle ZACB is right. point on the circle, B A Proof outline: 1. Let AB be the diameter of a circle centered at o and let C be any other point on the circle. A
In GeoGebra:
1. Use Thales' Theorem to construct a right triangle. Use a segment AB as the diameter of a circle. Then put a point C on the circle. Thales' theorem guarantees triangle ABC is a right triangle.
2. Construct pentagons on the sides of the right triangle. Use the regular polygon tool to construct a pentagon (5-sided figure) on each side of the right triangle. (Be careful about the order in which you select the first two vertices of the
regular polygon. Select them in the order that makes the pentagon appear on the outside of the right triangle.)
3. Conjecture a relationship between the pentagon areas. Use the area measuring tool and click on the three pentagons to display their areas. Take a screenshot and write a caption describing the relationship between the areas of the three
pentagons.
4. Explore other shapes. Repeat steps 2 and 3, replacing pentagons with:
a. equilateral triangles
b. hexagons
c. cirçles
d. any other shape of your choosing
5. Generalized Pythagorean Theorem. Make a conjecture: If similar shapes are constructed on the sides of a right triangle, then..
Transcribed Image Text:In GeoGebra: 1. Use Thales' Theorem to construct a right triangle. Use a segment AB as the diameter of a circle. Then put a point C on the circle. Thales' theorem guarantees triangle ABC is a right triangle. 2. Construct pentagons on the sides of the right triangle. Use the regular polygon tool to construct a pentagon (5-sided figure) on each side of the right triangle. (Be careful about the order in which you select the first two vertices of the regular polygon. Select them in the order that makes the pentagon appear on the outside of the right triangle.) 3. Conjecture a relationship between the pentagon areas. Use the area measuring tool and click on the three pentagons to display their areas. Take a screenshot and write a caption describing the relationship between the areas of the three pentagons. 4. Explore other shapes. Repeat steps 2 and 3, replacing pentagons with: a. equilateral triangles b. hexagons c. cirçles d. any other shape of your choosing 5. Generalized Pythagorean Theorem. Make a conjecture: If similar shapes are constructed on the sides of a right triangle, then..
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