Congruence
Congruence Theorems
Objectives:
- Identify congruent and non-congruent figures
- Identify corresponding parts given two congruent figures
- Write congruence statements given congruent figures
- Use the congruence theorems to determine if two figures are congruent
What is Congruence?
What does congruence mean?
Congruence means exactly the same size and shape. Two figures are congruent if and only if the figures have both the same size and shape.
Let's look at some examples below:
Congruence means exactly the same size and shape. Two figures are congruent if and only if the figures have both the same size and shape.
Let's look at some examples below:
Examples
Determine if the figures are congruent:
Definition: Corresponding Parts
What are corresponding parts?
Corresponding parts are angles or sides that are in the same relative position in both figures. We can determine the corresponding parts of two figures given a diagram or statement.
Corresponding parts are angles or sides that are in the same relative position in both figures. We can determine the corresponding parts of two figures given a diagram or statement.
Corresponding Parts Given a Diagram
Given the following diagram, we can determine the corresponding parts by looking at the "tick" marks on the sides and angles of the triangles.
Example
Using the diagram below, determine the six corresponding parts:
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Corresponding Parts Given a Congruence Statement
As stated earlier, we can also determine corresponding parts given a statement. A statement is used to show that two figures are congruent. For example, given the following statement,
This means that "A" corresponds with "D", "B" corresponds with "E", and "C" corresponds with "F".
I like to think of a pattern. Since the letters are color coded we can see that it goes red, blue, green and then repeats with red, blue, and green.
I like to think of a pattern. Since the letters are color coded we can see that it goes red, blue, green and then repeats with red, blue, and green.
Example
Given the congruence statement below, determine the six corresponding parts:
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Congruence Theorems
Finally, we can look at the 5 Congruence Theorems!
Click on the images below to learn more about each Congruence Theorem:
Click on the images below to learn more about each Congruence Theorem:
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Quiz
You will take the quiz after you have researched and taken notes on the 5 Congruence Theorems.
CLICK HERE FOR QUIZ
CLICK HERE FOR QUIZ