a. Answer Always True. Explanation Given: The following is the given statement- An equilateral triangle is isosceles. Calculation :- The statement is always True because in equilateral triangle all sides are equal and in isosceles any two sides need to be equal. b. To determine To tell whether the given statement is true Always, Sometimes or Never. Answer Sometimes True. Explanation Given: The following is the given statement- The number of diagonals in the polygon is the same as the number of sides. Calculation :- The number of sides will only equal the number of diagonals if the figure is a pentagon. In all other figures, the number of sides will never equal the number of diagonals. c. To determine To tell whether the given statement is true Always, Sometimes or Never. Answer Sometimes True. Explanation Given: The following is the given statement- An exterior angle of a triangle is larger in measure than any angle of a triangle. Calculation :- If the triangle is acute, the the exterior angle will be obtuse, and larger than any angle in the triangle. However, if the triangle is obtuse, then the exterior angle of the obtuse angle is acute, and therefore smaller than the obtuse angle d. To determine To tell whether the given statement is true Always, Sometimes or Never. Answer Never True. Explanation Given: The following is the given statement- One of the base angles of an isosceles triangle has a measure greater than that of one of the exterior angles of the triangle. Calculation :- If the triangle is isosceles, then the base angle has to be less than 90 degrees, because otherwise the measure of the angles of the triangle would be larger than 180

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 21RP

To determine

To tell whether the given statement is true Always, Sometimes or Never.

Expert Solution

Answer to Problem 21RP

Always True.

Explanation of Solution

Given:

The following is the given statement-

An equilateral triangle is isosceles.

Calculation:-

The statement is always True because in equilateral triangle all sides are equal and in isosceles any two sides need to be equal.

To determine

To tell whether the given statement is true Always, Sometimes or Never.

Expert Solution

Answer to Problem 21RP

Sometimes True.

Explanation of Solution

Given:

The following is the given statement-

The number of diagonals in the polygon is the same as the number of sides.

Calculation:-

The number of sides will only equal the number of diagonals if the figure is a pentagon. In all other figures, the number of sides will never equal the number of diagonals.

To determine

To tell whether the given statement is true Always, Sometimes or Never.

Expert Solution

Answer to Problem 21RP

Sometimes True.

Explanation of Solution

Given:

The following is the given statement-

An exterior angle of a triangle is larger in measure than any angle of a triangle.

Calculation:-

If the triangle is acute, the the exterior angle will be obtuse, and larger than any angle in the triangle. However, if the triangle is obtuse, then the exterior angle of the obtuse angle is acute, and therefore smaller than the obtuse angle

To determine

To tell whether the given statement is true Always, Sometimes or Never.

Expert Solution

Answer to Problem 21RP

Never True.

Explanation of Solution

Given:

The following is the given statement-

One of the base angles of an isosceles triangle has a measure greater than that of one of the exterior angles of the triangle.

Calculation:-

If the triangle is isosceles, then the base angle has to be less than 90 degrees, because otherwise the measure of the angles of the triangle would be larger than 180

Chapter 7, Problem 20RP

Chapter 7, Problem 22RP

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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