91st Edition

ISBN: 9780866099653

Author: Richard Rhoad, George Milauskas, Robert Whipple

Publisher: McDougal Littell

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Question

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 7, Problem 17RP

To determine

To prove : The congruency of the diagonals of a regular pentagon

Expert Solution & Answer

Explanation of Solution

Given information : The following information has been given

Regular pentagon

All angles are congruent

All sides are congruent

Formula used : Any two triangles are said to be congruent by SAS property if they have two congruent sides, and the angle containing then is also congruent

Proof : We know that as the pentagon is of sides, any diagonal will have only one vertex on one side of the diagonal, and only two vertices of pentagon on the other. There is no other possibility.

Thus, we assume a triangle with diagonal as one side and sides of pentagon as the other two.

We know that in a pentagon

All angles are congruent

All sides are congruent

Hence, we can say that all the triangles containing a diagonal will be congruent by SAS property.

Now, by virtue of congruency, we can say that the diagonal will be congruent always, for any sides it’s chosen for.

Hence, proven that the diagonals are congruent

Chapter 7, Problem 16RP

Chapter 7, Problem 18RP

Chapter 7 Solutions

Geometry For Enjoyment And Challenge

Ch. 7.1 - Prob. 1PSA Ch. 7.1 - Prob. 2PSA Ch. 7.1 - Prob. 3PSA Ch. 7.1 - Prob. 4PSA Ch. 7.1 - Prob. 5PSA Ch. 7.1 - Prob. 6PSA Ch. 7.1 - Prob. 7PSA Ch. 7.1 - Prob. 8PSA Ch. 7.1 - Prob. 9PSA Ch. 7.1 - Prob. 10PSA

Ch. 7.1 - Prob. 11PSA Ch. 7.1 - Prob. 12PSB Ch. 7.1 - Prob. 13PSB Ch. 7.1 - Prob. 14PSB Ch. 7.1 - Prob. 15PSB Ch. 7.1 - Prob. 16PSB Ch. 7.1 - Prob. 17PSB Ch. 7.1 - Prob. 18PSB Ch. 7.1 - Prob. 19PSC Ch. 7.1 - Prob. 20PSC Ch. 7.1 - Prob. 21PSC Ch. 7.1 - Prob. 22PSC Ch. 7.1 - Prob. 23PSC Ch. 7.2 - Prob. 1PSA Ch. 7.2 - Prob. 2PSA Ch. 7.2 - Prob. 3PSA Ch. 7.2 - Prob. 4PSA Ch. 7.2 - Prob. 5PSA Ch. 7.2 - Prob. 6PSA Ch. 7.2 - Prob. 7PSA Ch. 7.2 - Prob. 8PSA Ch. 7.2 - Prob. 9PSA Ch. 7.2 - Prob. 10PSA Ch. 7.2 - Prob. 11PSB Ch. 7.2 - Prob. 12PSB Ch. 7.2 - Prob. 13PSB Ch. 7.2 - Prob. 14PSB Ch. 7.2 - Prob. 15PSB Ch. 7.2 - Prob. 16PSB Ch. 7.2 - Prob. 17PSC Ch. 7.2 - Prob. 18PSC Ch. 7.2 - Prob. 19PSC Ch. 7.2 - Prob. 20PSD Ch. 7.3 - Prob. 1PSA Ch. 7.3 - Prob. 2PSA Ch. 7.3 - Prob. 3PSA Ch. 7.3 - Prob. 4PSA Ch. 7.3 - Prob. 5PSA Ch. 7.3 - Prob. 6PSA Ch. 7.3 - Prob. 7PSA Ch. 7.3 - Prob. 8PSB Ch. 7.3 - Prob. 9PSB Ch. 7.3 - Prob. 10PSB Ch. 7.3 - Prob. 11PSB Ch. 7.3 - Prob. 12PSB Ch. 7.3 - Prob. 13PSB Ch. 7.3 - Prob. 14PSB Ch. 7.3 - Prob. 15PSB Ch. 7.3 - Prob. 16PSB Ch. 7.3 - Prob. 17PSB Ch. 7.3 - Prob. 18PSB Ch. 7.3 - Prob. 19PSB Ch. 7.3 - Prob. 20PSC Ch. 7.3 - Prob. 21PSC Ch. 7.3 - Prob. 22PSC Ch. 7.3 - Prob. 23PSC Ch. 7.3 - Prob. 24PSD Ch. 7.4 - Prob. 1PSA Ch. 7.4 - Prob. 2PSA Ch. 7.4 - Prob. 3PSA Ch. 7.4 - Prob. 4PSA Ch. 7.4 - Prob. 5PSA Ch. 7.4 - Prob. 6PSA Ch. 7.4 - Prob. 7PSA Ch. 7.4 - Prob. 8PSB Ch. 7.4 - Prob. 9PSB Ch. 7.4 - Prob. 10PSB Ch. 7.4 - Prob. 11PSB Ch. 7.4 - Prob. 12PSB Ch. 7.4 - Prob. 13PSB Ch. 7.4 - Prob. 14PSC Ch. 7.4 - Prob. 15PSC Ch. 7.4 - Prob. 16PSC Ch. 7.4 - Prob. 17PSC Ch. 7 - Prob. 1RP Ch. 7 - Prob. 2RP Ch. 7 - Prob. 3RP Ch. 7 - Prob. 4RP Ch. 7 - Prob. 5RP Ch. 7 - Prob. 6RP Ch. 7 - Prob. 7RP Ch. 7 - Prob. 8RP Ch. 7 - Prob. 9RP Ch. 7 - Prob. 10RP Ch. 7 - Prob. 11RP Ch. 7 - Prob. 12RP Ch. 7 - Prob. 13RP Ch. 7 - Prob. 14RP Ch. 7 - Prob. 15RP Ch. 7 - Prob. 16RP Ch. 7 - Prob. 17RP Ch. 7 - Prob. 18RP Ch. 7 - Prob. 19RP Ch. 7 - Prob. 20RP Ch. 7 - Prob. 21RP Ch. 7 - Prob. 22RP Ch. 7 - Prob. 23RP Ch. 7 - Prob. 24RP Ch. 7 - Prob. 25RP Ch. 7 - Prob. 26RP Ch. 7 - Prob. 27RP Ch. 7 - Prob. 28RP Ch. 7 - Prob. 29RP Ch. 7 - Prob. 30RP

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