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Fun with Lines: Perpendicular and Angle Bisectors

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Colleensasser

10/24/2023

Geometry

Perpendicular Bisector Theorem and Angle Bisector Theorem Explained

Fun with Lines: Perpendicular and Angle Bisectors

The perpendicular and angle bisector theorems are fundamental geometric concepts that help solve complex geometric problems. This comprehensive guide explores key theorems and their practical applications in solving angle bisector problems and math perimeter calculations using bisectors.

• The perpendicular bisector theorem states that any point on a perpendicular bisector is equidistant from the endpoints of the segment it bisects

• The angle bisector theorem establishes that points on an angle bisector are equidistant from the sides of the angle

• Multiple perpendicular bisector theorem examples demonstrate practical applications in finding unknown lengths and angles

• The guide includes detailed problem-solving techniques for calculating perimeters and distances using these theorems

...

10/24/2023

66

3.5 Perpendicular & angle bisectors
VOCAB
PERPENDICULAR
- if a pointison the perpendicular
bisector of a
equidistant
segment
A
A
EXAMPLE
A)

View

Page 2: Angle Bisector Applications

This page explores the angle bisector theorem and its applications in solving complex geometric problems, particularly focusing on perimeter calculations.

Definition: The angle bisector theorem states that any point on an angle bisector is equidistant from the sides of the angle.

Example: A detailed problem demonstrates finding the perimeter of triangle ABC where various segments measure 18 and 10 units, resulting in a perimeter of 28 units.

Highlight: The page emphasizes the relationship between angle bisectors and the distances from points to the sides of angles, which is crucial for solving more complex geometric problems.

3.5 Perpendicular & angle bisectors
VOCAB
PERPENDICULAR
- if a pointison the perpendicular
bisector of a
equidistant
segment
A
A
EXAMPLE
A)

View

Page 3: Advanced Applications

This page presents advanced applications of both perpendicular and angle bisector theorems, featuring complex problems involving multiple angles and segments.

Example: A problem solving for 2XWZ involves working with expressions like 43x+3 and 8x-35, ultimately finding that 2XWZ = 24.

Highlight: The page demonstrates how to combine multiple geometric concepts, including angle measurements and algebraic expressions, to solve complex problems.

Vocabulary: Angle measurements are given in degrees, with specific angles measuring 39° and other key measurements including TK = 18 and LS = 34.

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Geometry

66

Oct 24, 2023

3 pages

Fun with Lines: Perpendicular and Angle Bisectors

user profile picture

Colleensasser

@colleeflowerr

The perpendicular and angle bisector theorems are fundamental geometric concepts that help solve complex geometric problems. This comprehensive guide explores key theorems and their practical applications in solving angle bisector problems and math perimeter calculations using bisectors.

• The... Show more

3.5 Perpendicular & angle bisectors
VOCAB
PERPENDICULAR
- if a pointison the perpendicular
bisector of a
equidistant
segment
A
A
EXAMPLE
A)

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Page 2: Angle Bisector Applications

This page explores the angle bisector theorem and its applications in solving complex geometric problems, particularly focusing on perimeter calculations.

Definition: The angle bisector theorem states that any point on an angle bisector is equidistant from the sides of the angle.

Example: A detailed problem demonstrates finding the perimeter of triangle ABC where various segments measure 18 and 10 units, resulting in a perimeter of 28 units.

Highlight: The page emphasizes the relationship between angle bisectors and the distances from points to the sides of angles, which is crucial for solving more complex geometric problems.

3.5 Perpendicular & angle bisectors
VOCAB
PERPENDICULAR
- if a pointison the perpendicular
bisector of a
equidistant
segment
A
A
EXAMPLE
A)

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Page 3: Advanced Applications

This page presents advanced applications of both perpendicular and angle bisector theorems, featuring complex problems involving multiple angles and segments.

Example: A problem solving for 2XWZ involves working with expressions like 43x+3 and 8x-35, ultimately finding that 2XWZ = 24.

Highlight: The page demonstrates how to combine multiple geometric concepts, including angle measurements and algebraic expressions, to solve complex problems.

Vocabulary: Angle measurements are given in degrees, with specific angles measuring 39° and other key measurements including TK = 18 and LS = 34.

3.5 Perpendicular & angle bisectors
VOCAB
PERPENDICULAR
- if a pointison the perpendicular
bisector of a
equidistant
segment
A
A
EXAMPLE
A)

Sign up to see the contentIt's free!

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Perpendicular Bisector Fundamentals

This page introduces the perpendicular bisector theorem and its converse, featuring practical examples of finding unknown values using these concepts.

Definition: A perpendicular bisector is a line that intersects a segment at a 90-degree angle and divides it into two equal parts.

Vocabulary: Equidistant means being at equal distances from two or more points or objects.

Example: In a problem solving for x, where 15x-7 = 3x+41, the solution demonstrates how to use algebraic manipulation alongside geometric principles to find x = 4.

Highlight: The converse perpendicular bisector theorem states that if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of that segment.

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

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Marco B

iOS user

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Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user