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Geometry proof problem: midpoint

How to Complete Segment Proofs in Geometry - Step by Step, With Angles, and Worksheets with Answers

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How to Complete Segment Proofs in Geometry - Step by Step, With Angles, and Worksheets with Answers
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Paylee

@paylee_zmgg

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140 Followers

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How to complete segment proofs in geometry step by step: A comprehensive guide to mastering segment proofs in geometry, including midpoint theorems, segment addition postulates, and congruence properties.

Key points:

  • Understand the given information and what needs to be proven
  • Use definitions, postulates, and properties to build logical steps
  • Apply the segment addition postulate and midpoint theorem effectively
  • Utilize congruence properties and transitive properties to establish relationships
  • Practice with various examples to reinforce understanding

3/6/2023

603

2.1.3b ATA 2.8b Segment Proofs Name: Statements 1. E is the mid point of DF 2. DE = EF FDE 3. DE+DE = DE + EF 4. 2DE DE + EF 5. DE+EF=DF 6.

View

Page 4: Advanced Applications of Segment Proofs

This page presents more complex applications of segment proofs, incorporating various geometric properties and postulates.

The tenth proof demonstrates how to prove that Q is the midpoint of PR given that 2PQ = PR. This proof uses the segment addition postulate and the subtraction property to establish that PQ = QR, which defines Q as the midpoint of PR.

The eleventh proof shows how to prove that AD = CE given that AB ≅ CD and BD ≅ DE. This proof combines the segment addition postulate with the transitive property to establish the equality of AD and CE.

Example: In the proof AB + BD = AD, CD + DE = CE, the segment addition postulate is applied twice to show that the sum of two adjacent segments is equal to the whole segment on both sides of the equation.

The twelfth proof demonstrates how to prove that HI ≅ JK given that GI ≅ JL and GH ≅ KL. This proof employs the segment addition property, substitution property, and subtraction property of equality to establish the congruence of HI and JK.

Vocabulary: The subtraction property of equality states that if you subtract the same quantity from both sides of an equation, the equation remains true.

These advanced proofs reinforce the importance of logical reasoning and the application of multiple geometric properties in solving complex segment problems.

2.1.3b ATA 2.8b Segment Proofs Name: Statements 1. E is the mid point of DF 2. DE = EF FDE 3. DE+DE = DE + EF 4. 2DE DE + EF 5. DE+EF=DF 6.

View

Page 1: Introduction to Segment Proofs

This page introduces the concept of segment proofs in geometry and provides several examples to illustrate the process.

The first proof demonstrates how to prove that 2DE = DF given that E is the midpoint of DF. The proof uses the definition of midpoint, the addition property of equality, and the segment addition postulate to establish the relationship.

Definition: A midpoint is a point that divides a line segment into two equal parts.

The second proof shows how to prove that L is the midpoint of KM given that KL ≅ LN and LM ≅ LN. This proof utilizes the transitive property of congruence to establish that KL ≅ LM, which leads to the conclusion that L is the midpoint of KM.

Example: In the proof KL ≅ LN, LM ≅ LN → KL ≅ LM, the transitive property of congruence is applied to show that two segments are congruent to a common segment, therefore they are congruent to each other.

The third proof demonstrates how to prove that PS ≅ TU given that PQ ≅ TQ and UQ ≅ QS. This proof employs the segment addition postulate and the definition of congruence to establish the relationship between the segments.

Highlight: The segment addition postulate states that the length of a whole segment is equal to the sum of the lengths of its parts.

2.1.3b ATA 2.8b Segment Proofs Name: Statements 1. E is the mid point of DF 2. DE = EF FDE 3. DE+DE = DE + EF 4. 2DE DE + EF 5. DE+EF=DF 6.

View

Page 2: Advanced Segment Proofs

This page presents more complex segment proofs, building on the concepts introduced in the previous page.

The fourth proof demonstrates how to prove that KL ≅ LM given that K is the midpoint of JL, M is the midpoint of LN, and JK ≅ MN. This proof combines the definition of midpoint with the transitive and symmetric properties of congruence.

Vocabulary: The symmetric property of congruence states that if A ≅ B, then B ≅ A.

The fifth proof shows how to prove that XZ = TV given that XY ≅ UV and YZ ≅ TU. This proof utilizes the segment addition property and substitution property to establish the equality of the segments.

The sixth proof demonstrates how to prove that XZ ≅ VW given that WY ≅ YZ and XY ≅ VY. This proof combines the segment addition postulate with the transitive property to establish the congruence of the segments.

Example: In the proof XY + YZ = XZ, VY + YW = VW, the segment addition postulate is applied to show that the sum of two adjacent segments is equal to the whole segment.

2.1.3b ATA 2.8b Segment Proofs Name: Statements 1. E is the mid point of DF 2. DE = EF FDE 3. DE+DE = DE + EF 4. 2DE DE + EF 5. DE+EF=DF 6.

View

Page 3: Midpoint Theorems and Congruence Properties

This page focuses on proofs involving midpoint theorems and congruence properties.

The seventh proof demonstrates how to prove that DE ≅ AE given that E is the midpoint of AC and DE = EC. This proof uses the definition of midpoint and the transitive property of equality to establish the congruence.

The eighth proof shows how to prove that S is the midpoint of RT given that RS = 1/2RT. This proof employs the multiplication property of equality and the segment addition postulate to establish that S divides RT into two equal parts.

Definition: The multiplication property of equality states that if you multiply both sides of an equation by the same number, the equation remains true.

The ninth proof demonstrates how to prove that LM ≅ NO given that M is the midpoint of LN and N is the midpoint of MO. This proof combines the definition of midpoint with the transitive property of equality to establish the congruence.

Highlight: The transitive property of equality states that if a = b and b = c, then a = c.

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

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

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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

/

Congruence

/

Proofs of general theorem

/

Geometry proof problem: midpoint

How to Complete Segment Proofs in Geometry - Step by Step, With Angles, and Worksheets with Answers

user profile picture

Paylee

@paylee_zmgg

·

140 Followers

Follow

How to complete segment proofs in geometry step by step: A comprehensive guide to mastering segment proofs in geometry, including midpoint theorems, segment addition postulates, and congruence properties.

Key points:

  • Understand the given information and what needs to be proven
  • Use definitions, postulates, and properties to build logical steps
  • Apply the segment addition postulate and midpoint theorem effectively
  • Utilize congruence properties and transitive properties to establish relationships
  • Practice with various examples to reinforce understanding

3/6/2023

603

 

Geometry

103

2.1.3b ATA 2.8b Segment Proofs Name: Statements 1. E is the mid point of DF 2. DE = EF FDE 3. DE+DE = DE + EF 4. 2DE DE + EF 5. DE+EF=DF 6.

Page 4: Advanced Applications of Segment Proofs

This page presents more complex applications of segment proofs, incorporating various geometric properties and postulates.

The tenth proof demonstrates how to prove that Q is the midpoint of PR given that 2PQ = PR. This proof uses the segment addition postulate and the subtraction property to establish that PQ = QR, which defines Q as the midpoint of PR.

The eleventh proof shows how to prove that AD = CE given that AB ≅ CD and BD ≅ DE. This proof combines the segment addition postulate with the transitive property to establish the equality of AD and CE.

Example: In the proof AB + BD = AD, CD + DE = CE, the segment addition postulate is applied twice to show that the sum of two adjacent segments is equal to the whole segment on both sides of the equation.

The twelfth proof demonstrates how to prove that HI ≅ JK given that GI ≅ JL and GH ≅ KL. This proof employs the segment addition property, substitution property, and subtraction property of equality to establish the congruence of HI and JK.

Vocabulary: The subtraction property of equality states that if you subtract the same quantity from both sides of an equation, the equation remains true.

These advanced proofs reinforce the importance of logical reasoning and the application of multiple geometric properties in solving complex segment problems.

2.1.3b ATA 2.8b Segment Proofs Name: Statements 1. E is the mid point of DF 2. DE = EF FDE 3. DE+DE = DE + EF 4. 2DE DE + EF 5. DE+EF=DF 6.

Page 1: Introduction to Segment Proofs

This page introduces the concept of segment proofs in geometry and provides several examples to illustrate the process.

The first proof demonstrates how to prove that 2DE = DF given that E is the midpoint of DF. The proof uses the definition of midpoint, the addition property of equality, and the segment addition postulate to establish the relationship.

Definition: A midpoint is a point that divides a line segment into two equal parts.

The second proof shows how to prove that L is the midpoint of KM given that KL ≅ LN and LM ≅ LN. This proof utilizes the transitive property of congruence to establish that KL ≅ LM, which leads to the conclusion that L is the midpoint of KM.

Example: In the proof KL ≅ LN, LM ≅ LN → KL ≅ LM, the transitive property of congruence is applied to show that two segments are congruent to a common segment, therefore they are congruent to each other.

The third proof demonstrates how to prove that PS ≅ TU given that PQ ≅ TQ and UQ ≅ QS. This proof employs the segment addition postulate and the definition of congruence to establish the relationship between the segments.

Highlight: The segment addition postulate states that the length of a whole segment is equal to the sum of the lengths of its parts.

2.1.3b ATA 2.8b Segment Proofs Name: Statements 1. E is the mid point of DF 2. DE = EF FDE 3. DE+DE = DE + EF 4. 2DE DE + EF 5. DE+EF=DF 6.

Page 2: Advanced Segment Proofs

This page presents more complex segment proofs, building on the concepts introduced in the previous page.

The fourth proof demonstrates how to prove that KL ≅ LM given that K is the midpoint of JL, M is the midpoint of LN, and JK ≅ MN. This proof combines the definition of midpoint with the transitive and symmetric properties of congruence.

Vocabulary: The symmetric property of congruence states that if A ≅ B, then B ≅ A.

The fifth proof shows how to prove that XZ = TV given that XY ≅ UV and YZ ≅ TU. This proof utilizes the segment addition property and substitution property to establish the equality of the segments.

The sixth proof demonstrates how to prove that XZ ≅ VW given that WY ≅ YZ and XY ≅ VY. This proof combines the segment addition postulate with the transitive property to establish the congruence of the segments.

Example: In the proof XY + YZ = XZ, VY + YW = VW, the segment addition postulate is applied to show that the sum of two adjacent segments is equal to the whole segment.

2.1.3b ATA 2.8b Segment Proofs Name: Statements 1. E is the mid point of DF 2. DE = EF FDE 3. DE+DE = DE + EF 4. 2DE DE + EF 5. DE+EF=DF 6.

Page 3: Midpoint Theorems and Congruence Properties

This page focuses on proofs involving midpoint theorems and congruence properties.

The seventh proof demonstrates how to prove that DE ≅ AE given that E is the midpoint of AC and DE = EC. This proof uses the definition of midpoint and the transitive property of equality to establish the congruence.

The eighth proof shows how to prove that S is the midpoint of RT given that RS = 1/2RT. This proof employs the multiplication property of equality and the segment addition postulate to establish that S divides RT into two equal parts.

Definition: The multiplication property of equality states that if you multiply both sides of an equation by the same number, the equation remains true.

The ninth proof demonstrates how to prove that LM ≅ NO given that M is the midpoint of LN and N is the midpoint of MO. This proof combines the definition of midpoint with the transitive property of equality to establish the congruence.

Highlight: The transitive property of equality states that if a = b and b = c, then a = c.

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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