• Student Access
  • CONTACT
MATH IN DEMAND
  • Student Access
  • CONTACT
MATH IN DEMAND

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:

Examples

Determine if the figures are congruent:
Picture
Click HERE to see answer
Picture
Click HERE to see answer
Picture
Click HERE to see answer


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 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.
Picture
Picture
Picture

Example

Using the diagram below, determine the six corresponding parts:
Picture
Click HERE to check your answer

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,
Picture
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.
Picture

Example

Given the congruence statement below, determine the six corresponding parts:
Picture
Click HERE to check your answer

Congruence Theorems

Picture
Finally, we can look at the 5 Congruence Theorems!
​Click on the images below to learn more about each Congruence Theorem:
Picture
Picture
Picture
Picture
Picture

Quiz

You will take the quiz after you have researched and taken notes on the 5 Congruence Theorems.
​CLICK HERE FOR QUIZ
(C) 2025 MATH IN DEMAND​