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Fun with Lines: Perpendicular and Angle Bisectors

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Fun with Lines: Perpendicular and Angle Bisectors
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Colleensasser

@colleeflowerr

·

16 Followers

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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

57

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.

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 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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Fun with Lines: Perpendicular and Angle Bisectors

user profile picture

Colleensasser

@colleeflowerr

·

16 Followers

Follow

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

57

 

10th

 

Geometry

3

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

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)

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)

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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying