C - Congruent Triangles Lesson

Congruent Figures

Rigid transformations are transformations that do not change the shape of the figure, or the size, only the location or orientation. Which of the following are rigid transformations?

Translation: Rigid

Reflection: Rigid 

Rotation: Rigid

Dilation: Not rigid

Figure ABCD can be mapped onto figure QRST by a series of rigid transformations.

First, you would translate ABCD until point A coincides with what point?

• Solution: Point Q

Next, you would rotate it until side AB coincides with which side?

• Solution: Side QR

Third, you would reflect over which side?

• Solution: Reflect of side AB (or QR)

One definition of congruence is that you can map one figure on to another by a series of rigid transformations (translations, rotations and reflections).  

Transform Triangle ABC by a series of rigid transformations. Use a translation, a rotation and a reflection (You may need to trace the triangle). Did any of your sides change length? Did any of your angles change measure?

Congruent Triangle Exploration

Just as there are criteria used to determine if triangles are similar, there are also criteria for determining triangles are congruent.   In the congruent triangle exploration, you will use rigid transformations to investigate what criteria are sufficient to determine that triangles are congruent.

Although we will explore other types of proofs, a vast majority of the proofs in this module will be based on congruent triangles. In this lesson you will learn multiple methods of proving that two triangles are congruent. In order for two triangles to be congruent, all corresponding sides and all corresponding angles must be congruent. But wouldn't it be nice if we did not have to prove ALL the corresponding sides and angles congruent in order to prove that the triangles are congruent? You can get by with less.

Now test your knowledge of congruent triangle criteria with the following activity.

 

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