drawing the pictures works 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. circles d. any other shape of your choosing5. **Generalized Pythagorean Theorem.** Make a conjecture: *If similar shapes are constructed on the sides of a right triangle, then …* Thales' TheoremIf $\overline{AB}$ is the diameter of a circle centered at $O$ and $C$ is any other point on the circle, then the angle $\angle ACB$ is right.![Diagram](link-to-diagram.png)The diagram above illustrates a circle with center $O$. The line segment $\overline{AB}$ is the diameter, and point $C$ is located on the circumference of the circle. The angle $\angle ACB$ formed by the points $A$, $C$, and $B$ is a right angle (90 degrees).Proof Outline:1. Let $\overline{AB}$ be the diameter of a circle centered at $O$ and let $C$ be any other point on the circle.![Diagram](link-to-diagram.png)In this part of the diagram, similar to the previous one, line segment $\overline{AB}$ is drawn as the diameter of the circle. Point $C$ is again on the circumference, forming a triangle with points $A$ and $B$. The theorem assures that $\angle ACB$ is a right angle.

Answered: drawing the pictures works

Math

Advanced Math

drawing the pictures works

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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