Sample Problem Solution

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Sample Problem Solution

• Part of a mathematics lesson prepared by
• Rod Rowell, M.A.
• (edited for demonstration purposes)

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Step By Step Practice

• In this exercise you will be asked questions
  about a proof that will help you write the proof.
• Please click the mouse to continue.

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Step By Step Practice

• Please click on a problem.
• Sample Problem One

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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
Click the mouse to continue.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
Start by marking the different items congruent in
the diagram.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
Start by marking the different items congruent in
the diagram.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
Start by marking the different items congruent in
the diagram. What are the key words or symbols?
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
Start by marking the different items congruent in
the diagram. What are the key words or
symbols? The only key symbol is ?, and we have
already marked the diagram with the congruent
items .
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
Start by marking the different items congruent in
the diagram. What are the key words or
symbols? The only key symbol is ?, and we have
already marked the diagram with the congruent
items . Now, choose a method the prove the
triangles congruent.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
In order to determine what method to use, answer
the following questions.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
In order to determine what method to use, answer
the following questions. Do the triangles share
any sides or angles?
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
In order to determine what method to use, answer
the following questions. Do the triangles share
any sides or angles? The triangles share side
AB and AB is congruent to itself by the
reflexive property.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
In order to determine what method to use, answer
the following questions. Do the triangles share
any sides or angles? The triangles share side
AB and AB is congruent to itself by the
reflexive property.
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Sample Problem One
G CE ? ED AE ? EB ltCAE ? ltDBE
ltEAB ? ltEBA P DCAB ? DDBA
In order to determine what method to use, answer
the following questions. Do the triangles
contain any corresponding congruent angles?
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
In order to determine what method to use, answer
the following questions. Do the triangles
contain any corresponding congruent
angles? Yes, ltEAB ? ltEBA
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
In order to determine what method to use, answer
the following questions. Do the triangles
contain any corresponding congruent segments?
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
In order to determine what method to use, answer
the following questions. Do the triangles
contain any corresponding congruent
segments? Notice how AE and ED add to form AD.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
In order to determine what method to use, answer
the following questions. Do the triangles
contain any corresponding congruent
segments? Notice how AE and ED add to form
AD. Notice how CE and EB add to form CB.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
In order to determine what method to use, answer
the following questions. Do the triangles
contain any corresponding congruent
segments? Notice how AE and ED add to form
AD. Notice how CE and EB add to form CB. What
theorem could be used to show AD ? CB?
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
In order to determine what method to use, answer
the following questions. Do the triangles
contain any corresponding congruent
segments? Notice how AE and ED add to form
AD. Notice how CE and EB add to form CB. What
theorem could be used to show AD ? CB? If
congruent segments are added to congruent
segments, the sums are congruent.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
What method can be used to show DCAB ? DDBA?
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
What method can be used to show DCAB ? DDBA? We
know that two sets of corresponding sides and the
included angles are congruent.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
What method can be used to show DCAB ? DDBA? We
know that two sets of corresponding sides and the
included angles are congruent. Use SAS to show
DCAB ? DDBA.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
What method can be used to show DCAB ? DDBA? We
know that two sets of corresponding sides and the
included angles are congruent. Use SAS to show
DCAB ? DDBA. Now, write the proof.
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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
Statements
Reasons
1. CE ? ED 1. Given 2. AE ? EB 2. Given 3.
ltEAB ? ltEBA 3. Given

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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
Statements
Reasons
1. CE ? ED 1. Given 2. AE ? EB 2. Given 3.
ltEAB ? ltEBA 3. Given 4. AB ? AB 4. Reflexive

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Sample Problem One
G CE ? ED AE ? EB ltEAB ? ltEBA P DCAB
? DDBA
Statements
Reasons
1. CE ? ED 1. Given 2. AE ? EB 2. Given 3.
ltEAB ? ltEBA 3. Given 4. AB ? AB 4.
Reflexive 5. AD ? CB 5. If congruent segments
are added to to congruent segments,
the sums are congruent.

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Good Job!
Note Other sample problems and guided
solutions included in this lesson have been
deleted to save space.
The End