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Chapter 4.CR, Problem 23CR
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### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# Review ExercisesIn Review Exercises 22 to 24, M and N are the midpoints of F J - and F H - respectively. Given: J H = 12 m ∠ J = 80 ° m ∠ F = 60 ° Prove: M N ,   m ∠ F M N ,   m ∠ F N M

To determine

To Find:

The length of the line joining the mid points of the sides of the triangle and measure of angles based on the information provided.

Explanation

Formula Used:

Sum of the interior angle of a triangle is 180Â°.

Theorem on triangle:

The line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one-half the length of the third side.

That is, âˆ†ABC with midpoints M and N of AB- and AC-, respectively. Then MN-âˆ¥BC-. It can be concluded that BC=12(MN)

Calculation:

It is given that âˆ†FJH is an isosceles triangle with M and N are the midpoints of FJ- and FH- respectively.

Also given that JH=12, mâˆ J=80Â° and mâˆ F=60Â°.

Applying the theorem, MN is parallel to JH.

So mâˆ FHJ=mâˆ FNM and mâˆ FJH=mâˆ FMN.

Here mâˆ J=80Â°

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#### True or False: If f(x) = F(x), then baf(x)dx=F(b)F(a).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
The provided text is a part of a textbook problem and solution, specifically from a geometry textbook. It describes a problem where the student is asked to find the length of a line segment joining the midpoints of two sides of a triangle and the measures of certain angles, given the lengths and measures of other sides and angles of the triangle.
no_question

the text itself does not contain a direct question or an answer to a mathematical question. instead, it provides a problem statement and a partial solution, which would typically be followed by a detailed step-by-step solution in the textbook.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
menu
Hit Return to see all results
Chapter 4.CR, Problem 23CR
BuyFindarrow_forward

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# Review ExercisesIn Review Exercises 22 to 24, M and N are the midpoints of F J - and F H - respectively. Given: J H = 12 m ∠ J = 80 ° m ∠ F = 60 ° Prove: M N ,   m ∠ F M N ,   m ∠ F N M

To determine

To Find:

The length of the line joining the mid points of the sides of the triangle and measure of angles based on the information provided.

Explanation

Formula Used:

Sum of the interior angle of a triangle is 180Â°.

Theorem on triangle:

The line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one-half the length of the third side.

That is, âˆ†ABC with midpoints M and N of AB- and AC-, respectively. Then MN-âˆ¥BC-. It can be concluded that BC=12(MN)

Calculation:

It is given that âˆ†FJH is an isosceles triangle with M and N are the midpoints of FJ- and FH- respectively.

Also given that JH=12, mâˆ J=80Â° and mâˆ F=60Â°.

Applying the theorem, MN is parallel to JH.

So mâˆ FHJ=mâˆ FNM and mâˆ FJH=mâˆ FMN.

Here mâˆ J=80Â°

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Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

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## Additional Math Solutions

#### Find more solutions based on key concepts

Show solutions add

#### True or False: If f(x) = F(x), then baf(x)dx=F(b)F(a).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
user
The provided text is a part of a textbook problem and solution, specifically from a geometry textbook. It describes a problem where the student is asked to find the length of a line segment joining the midpoints of two sides of a triangle and the measures of certain angles, given the lengths and measures of other sides and angles of the triangle.

TYPE: NO_QUESTION

The text itself does not contain a direct question or an answer to a mathematical question. Instead, it provides a problem statement and a partial solution, which would typically be followed by a detailed step-by-step solution in the textbook.