Explanation Procedure used: The locus of points in a plane and equidistant from the sides of an angle is the angle bisector. Proof: 1) If a point is on the angle bisector, then it is equidistant from the sides of the angle. In the following figure, the bisector B D divides the angle ∠ A B C and the point D lies on the bisector B D . D E - ⊥ A B → and D F - ⊥ B C → . Since B D → bisects ∠ A B C , ∠ A B D = ∠ C B D . Since, D E - ⊥ A B → and D F - ⊥ B C → , ∠ D E B = ∠ D F B ≅ right triangles. By identity, B D ¯ ≅ B D ¯ . By AAS, ∠ D E B ≅ ∠ D F B then D E ¯ ≅ D F ¯ by CPCTC. 2) If a point is equidistant from the sides of an angle, then it is on the angle bisector. In the above figure, the point D is equidistant from the sides of ∠ A B C . ∠ A B C such that D E - ⊥ A B → , D F - ⊥ B C → and D E - = D F - . Since B D → bisects ∠ A B C , the point D lies on the bisector of ∠ A B C . Since, D E - ⊥ A B → and D F - ⊥ B C → , ∠ D E B = ∠ D F B ≅ right triangles

Elementary Geometry For College Students, 7e

7th Edition

ISBN: 9781337614085

Author: Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher: Cengage,

See similar textbooks

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Videos

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 7.1, Problem 38E

To determine

To justify:

A perpendicular to a line from a point not on the line.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.1, Problem 37E

Chapter 7.1, Problem 39E

Chapter 7 Solutions

Elementary Geometry For College Students, 7e

Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Prob. 3E Ch. 7.1 - In Exercises 3 to 8, use the drawing provided....Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...Ch. 7.1 - Note: Exercises preceded by an asterisk are of a...

Knowledge Booster

$Geometry$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

To justify: A perpendicular to a line from a point not on the line.

Solution Summary: The author explains how the construction of a perpendicular to the line is explained by the angle bisector.