Congruent Figures
Visually Defined w/ 9 Fantastic Examples!

What are congruent figures?

Don’t worry if you’re not sure, because that’s exactly what we’re going to explore in today’s geometry lesson.

You’ll learn how to identify congruent figures, write congruence statements, and find the missing values given a congruency statement.

Let’s dive in!

Congruent figures must have the same size and the same shape. In other words, you can fit one on top of the other so that the two figures match exactly.

Let’s take a closer look at the example below.

You’ll notice that triangle ABC and triangle DEF are identical. More specifically their side lengths and their angle measures are all the same, therefore we can consider them congruent figures.

And that’s exactly how you prove two figures are congruent by matching their corresponding parts.

In the video below, we’re going to deep dive into harder examples which have unknown sides and angles.

Stay tuned!

Before we get there, let’s briefly discuss writing congruence statements, because order matters!

Using our previous image, we are now going to write all six congruency statements for the two given triangles:

1. Triangle ABC is congruent to Triangle DEF
2. Triangle ACB is congruent to Triangle DFE
3. Triangle BAC is congruent to Triangle EDF
4. Triangle BCA is congruent to Triangle EFD
5. Triangle CAB is congruent to Triangle FDE
6. Triangle CBA is congruent to Triangle FED

And we can use this method to write congruency statements for not just triangles, but for quadrilaterals and other polygons. We focus on the vertices, and we list corresponding vertices in the same order, as ck-12 accurately states.

And please note, that depending on which vertex we start with, and the direction we take around the figure will allow for various congruency statements.

In this geometry video we will:

1. Successfully determine if two figures are congruent.
2. Write congruence statements.
3. And lay the groundwork for writing a two-column proof for congruent figures.

Congruent Figures – Lesson & Examples (Video)

41 min

• Introduction to identifying congruent figures
• 00:00:26 – How to identify congruent figures? How to write congruency statements?
• Exclusive Content for Member’s Only

• 00:06:47 – Write a congruence statement for the pair of congruent figures (Examples #1-4)
• 00:18:54 – Write a congruence statement for the pair of congruent figures (Examples #5-6)
• 00:27:30 – Find x and y given pair of congruent quadrilaterals (Example #7)
• 00:31:04 – Find x and y given pair of congruent triangles (Example #8)
• 00:33:43 – Give the reason for each statement (Example #9)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions