Subjects

Geometry

Tranformations & translations

Symmetry

Fun with Geometry: Undefined Terms & Angle Adventures

Name: Knowunity
Brand: Knowunity

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Fun with Geometry: Undefined Terms & Angle Adventures

Mika

@ika_kali

0 Follower

A comprehensive guide to fundamental geometric concepts, focusing on undefined terms in geometry, points, lines, planes, segments, angles, and coordinate geometry. The material covers essential postulates, measurements, and formulas crucial for understanding basic geometry.

Introduces the 3 undefined terms in geometry: points, lines, and planes
Explores segment addition and angle measurements with detailed examples
Covers angle classifications and relationships between different types of angles
Details coordinate geometry concepts including midpoint and distance formulas
Provides practical examples and step-by-step problem-solving techniques

10/27/2023

1.3 Points, Linus, & Planes
Undefined Terms i
-Points (location)
line's
planes
Exi
.A
Descriptions li
point has no dimension (no length, wid

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1.5 Angles & Their Measure

This section introduces angles, their components, and classification based on their measures. It also covers the Angle Addition Postulate and provides examples of angle calculations.

Definition: An angle consists of two different rays with a common endpoint called the vertex. The interior of an angle contains all points between its two sides.

Vocabulary:

Acute angle: An angle measuring less than 90°
Right angle: An angle measuring exactly 90°
Obtuse angle: An angle measuring more than 90° but less than 180°
Straight angle: An angle measuring exactly 180°

Example: The Angle Addition Postulate states that if P is in the interior of ∠ABC, then m∠ABC = m∠ABP + m∠PBC.

Highlight: Understanding different types of angle classifications is essential for solving geometric problems and constructing proofs.

View

1.7 Midpoint and Distance Formulas

This section introduces formulas for finding midpoints on a number line and in the coordinate plane, as well as the distance formula for calculating the distance between two points.

Definition: The midpoint formula for a line segment AB with endpoints (x₁, y₁) and (x₂, y₂) is: Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Example: Find the midpoint of a line segment with endpoints at (3, -2) and (10, -6).

The distance formula is also introduced:

Definition: The distance between two points A(x₁, y₁) and B(x₂, y₂) is: d = √((x₂ - x₁)² + (y₂ - y₁)²)

Highlight: These formulas are essential tools for solving problems in coordinate geometry and are frequently used in more advanced geometric concepts.

View

1.3 Points, Lines, & Planes

This section introduces fundamental geometric terms and undefined concepts in geometry. It covers the basic building blocks of geometric figures and their properties.

Definition: Points, lines, and planes are considered undefined terms in geometry as they are the most basic concepts from which all other geometric ideas are built.

Vocabulary:

Coplanar points: Points that lie on the same plane
Colinear points: Points that lie on the same line

The section also introduces important geometric postulates:

Through any two points, there is exactly one line.
If two distinct lines intersect, they intersect at exactly one point.
If two distinct planes intersect, they intersect in exactly one line.
Through any three noncollinear points, there is exactly one plane.

Example: A point has no dimension but has a location. A line extends infinitely in both directions and has one dimension (length). A plane extends infinitely in two dimensions (length and width) without thickness.

Highlight: Understanding these undefined concepts in geometry is crucial for building a strong foundation in geometric reasoning and proofs.

View

1.6 Angle Pairs

This section explores various types of angle pairs and their relationships. It introduces important concepts such as adjacent angles, vertical angles, and complementary and supplementary angles.

Vocabulary:

Adjacent angles: Two angles that share a common side and vertex with no interior points in common
Vertical angles: Two angles whose sides form opposite rays
Linear pair: Two adjacent angles whose non-common sides are opposite rays
Complementary angles: Two angles whose measures have a sum of 90°
Supplementary angles: Two angles whose measures have a sum of 180°
Angle bisector: A ray that divides an angle into two congruent adjacent angles

Example: If two angles form a linear pair and one angle measures 69°, while the other is expressed as 5x - 46°, find the value of x.

Highlight: Recognizing and understanding these angle relationships is crucial for solving more complex geometric problems and proofs.

View

1.4 Segments & Their Measure

This section delves into line segments, their properties, and the Segment Addition Postulate. It also introduces the concept of congruent segments and the Ruler Postulate.

Definition: The Segment Addition Postulate states that if point B is between points A and C on a line, then AB + BC = AC.

Vocabulary:

Congruent segments: Segments that have the same length
Midpoint: A point that divides a segment into two congruent segments

The section provides several examples of applying the Segment Addition Postulate to solve problems involving segment lengths.

Example: If MP is 47 units long, and MN = 5x + 1 and NP = 11x - 2, find the values of MN and NP.

Highlight: The Ruler Postulate establishes a one-to-one correspondence between points on a line and real numbers, allowing us to measure distances between points.

View

Distance Formula Applications

This final section focuses on applying the distance formula to solve various geometric problems in the coordinate plane.

Example: Find the distance between the points (6, -4) and (11, -5).

The section provides step-by-step solutions to distance problems, reinforcing the application of the formula in different scenarios.

Highlight: Mastering the distance formula is crucial for analyzing geometric figures in the coordinate plane and solving real-world problems involving distances between points.

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.

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

Subjects

Geometry

Tranformations & translations

Symmetry

Fun with Geometry: Undefined Terms & Angle Adventures

Mika

@ika_kali

0 Follower

Introduces the 3 undefined terms in geometry: points, lines, and planes
Explores segment addition and angle measurements with detailed examples
Covers angle classifications and relationships between different types of angles
Details coordinate geometry concepts including midpoint and distance formulas
Provides practical examples and step-by-step problem-solving techniques

10/27/2023

9th/10th

Geometry

1.5 Angles & Their Measure

This section introduces angles, their components, and classification based on their measures. It also covers the Angle Addition Postulate and provides examples of angle calculations.

Definition: An angle consists of two different rays with a common endpoint called the vertex. The interior of an angle contains all points between its two sides.

Vocabulary:

Acute angle: An angle measuring less than 90°
Right angle: An angle measuring exactly 90°
Obtuse angle: An angle measuring more than 90° but less than 180°
Straight angle: An angle measuring exactly 180°

Example: The Angle Addition Postulate states that if P is in the interior of ∠ABC, then m∠ABC = m∠ABP + m∠PBC.

Highlight: Understanding different types of angle classifications is essential for solving geometric problems and constructing proofs.

1.7 Midpoint and Distance Formulas

This section introduces formulas for finding midpoints on a number line and in the coordinate plane, as well as the distance formula for calculating the distance between two points.

Definition: The midpoint formula for a line segment AB with endpoints (x₁, y₁) and (x₂, y₂) is: Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Example: Find the midpoint of a line segment with endpoints at (3, -2) and (10, -6).

The distance formula is also introduced:

Definition: The distance between two points A(x₁, y₁) and B(x₂, y₂) is: d = √((x₂ - x₁)² + (y₂ - y₁)²)

Highlight: These formulas are essential tools for solving problems in coordinate geometry and are frequently used in more advanced geometric concepts.

1.3 Points, Lines, & Planes

This section introduces fundamental geometric terms and undefined concepts in geometry. It covers the basic building blocks of geometric figures and their properties.

Definition: Points, lines, and planes are considered undefined terms in geometry as they are the most basic concepts from which all other geometric ideas are built.

Vocabulary:

Coplanar points: Points that lie on the same plane
Colinear points: Points that lie on the same line

The section also introduces important geometric postulates:

Through any two points, there is exactly one line.
If two distinct lines intersect, they intersect at exactly one point.
If two distinct planes intersect, they intersect in exactly one line.
Through any three noncollinear points, there is exactly one plane.

Example: A point has no dimension but has a location. A line extends infinitely in both directions and has one dimension (length). A plane extends infinitely in two dimensions (length and width) without thickness.

Highlight: Understanding these undefined concepts in geometry is crucial for building a strong foundation in geometric reasoning and proofs.

1.6 Angle Pairs

This section explores various types of angle pairs and their relationships. It introduces important concepts such as adjacent angles, vertical angles, and complementary and supplementary angles.

Vocabulary:

Adjacent angles: Two angles that share a common side and vertex with no interior points in common
Vertical angles: Two angles whose sides form opposite rays
Linear pair: Two adjacent angles whose non-common sides are opposite rays
Complementary angles: Two angles whose measures have a sum of 90°
Supplementary angles: Two angles whose measures have a sum of 180°
Angle bisector: A ray that divides an angle into two congruent adjacent angles

Example: If two angles form a linear pair and one angle measures 69°, while the other is expressed as 5x - 46°, find the value of x.

Highlight: Recognizing and understanding these angle relationships is crucial for solving more complex geometric problems and proofs.

1.4 Segments & Their Measure

This section delves into line segments, their properties, and the Segment Addition Postulate. It also introduces the concept of congruent segments and the Ruler Postulate.

Definition: The Segment Addition Postulate states that if point B is between points A and C on a line, then AB + BC = AC.

Vocabulary:

Congruent segments: Segments that have the same length
Midpoint: A point that divides a segment into two congruent segments

The section provides several examples of applying the Segment Addition Postulate to solve problems involving segment lengths.

Example: If MP is 47 units long, and MN = 5x + 1 and NP = 11x - 2, find the values of MN and NP.

Highlight: The Ruler Postulate establishes a one-to-one correspondence between points on a line and real numbers, allowing us to measure distances between points.

Distance Formula Applications

This final section focuses on applying the distance formula to solve various geometric problems in the coordinate plane.

Example: Find the distance between the points (6, -4) and (11, -5).

The section provides step-by-step solutions to distance problems, reinforcing the application of the formula in different scenarios.

Highlight: Mastering the distance formula is crucial for analyzing geometric figures in the coordinate plane and solving real-world problems involving distances between points.

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.

Download in

Google Play

Download in

App Store

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

Fun with Geometry: Undefined Terms & Angle Adventures

1.5 Angles & Their Measure

1.7 Midpoint and Distance Formulas

1.3 Points, Lines, & Planes

1.6 Angle Pairs

1.4 Segments & Their Measure

Distance Formula Applications

Similar Content

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.

4.9+

13 M

#1

950 K+

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

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

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

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

Fun with Geometry: Undefined Terms & Angle Adventures

1.5 Angles & Their Measure

1.7 Midpoint and Distance Formulas

1.3 Points, Lines, & Planes

1.6 Angle Pairs

1.4 Segments & Their Measure

Distance Formula Applications

Similar Content

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.

4.9+

13 M

#1

950 K+

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

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

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

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