Explanation Given: The provided statement is “A radius perpendicular to the chord bisects the arc of that chord”. Theorem used: Hypotenuse Leg theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and the leg of a second right triangle, then the triangles are congruent. Proof: Consider a circle with center O. Let A B ¯ be the chord and O D ¯ be the radius. We have to prove the radius perpendicular to the chord bisects the arc of that chord. That is to prove O D ¯ bisects A B ¯ . Draw radii O A ¯ and O B ¯ . Consider the triangles OCA and OCB . Since the radii of the circle are equal, we can say O A ¯ ≅ O B ¯

Elementary Geometry for College Students

6th Edition

ISBN: 9781285195698

Author: Daniel C. Alexander, Geralyn M. Koeberlein

Publisher: Cengage Learning

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 6.1, Problem 35E

To determine

To prove:

The statement “A radius perpendicular to the chord bisects the arc of that chord”.

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Chapter 6.1, Problem 34E

Chapter 6.1, Problem 36E

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To prove: The statement “A radius perpendicular to the chord bisects the arc of that chord”.

Solution Summary: The author explains the hypotenuse leg theorem, which proves that a radius perpendicular to the chord bisects the arc of that chord.