Q7. In the following diagram HL炉聽a... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 1: Q7. (page 15)

In the following diagram $\overset{炉}{H L}$ and $\overset{鈫�}{K T}$ intersect at the midpoint of $\overset{炉}{H L}$ . Classify the following statement as true or false.
$\overset{炉}{M T}$ bisects $\overset{炉}{L H}$ .

Short Answer

Expert verified

The statement $\overset{炉}{M T}$ bisects $\overset{炉}{L H}$ is true.

Step by step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of midpoint.

A midpoint is a point lying between two points and is in the middle of the line joining the two points.

Here the statement $\overset{炉}{L M} 鈮� \overset{炉}{M H}$ implies that the length of the line segment $\overset{炉}{L M}$ is equal to the length of the line segment $\overset{炉}{M H}$ such that $\overset{炉}{L M} = \overset{炉}{M H}$ .

Step 3. Step description.

As $\overset{炉}{H L}$ and $\overset{鈫�}{K T}$ intersect at the midpoint of $\overset{炉}{H L}$ and that intersection point is $M$ , thus $M$ is the midpoint of $\overset{炉}{H L}$ .

This implies that $\overset{鈫�}{K T}$ bisects $\overset{炉}{L H}$ and $\overset{炉}{M T}$ is also a part of $\overset{鈫�}{K T}$ and its one endpoint is the mid-point of $\overset{炉}{L H}$ , so it is true that $\overset{炉}{M T}$ bisect $\overset{炉}{L H}$ .