Wize High School Geometry Textbook (Common Core) > Congruent & Similar Triangles

Congruent Triangles

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Congruent Triangles
Congruent triangles are triangles that are the exact same:
all corresponding angles are the same, and 
the corresponding sides are the same
We say that △ABC≅△PQR\triangle ABC\cong\triangle PQR△ABC≅△PQR ("triangle ABC is congruent to triangle PQR")

Wize Tip
We must write the letters in the triangle so that the same angles match up!

For example, we shouldn't say △ABC≅△RQP\triangle ABC \cong \triangle RQP△ABC≅△RQP.


Watch Out!
Don't be fooled! 

Even if you rotate or flip the triangle, as long as the corresponding angles and corresponding sides are the same, they are still congruent triangles!


△ABC≅△PQR\triangle ABC \cong \triangle PQR△ABC≅△PQR
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Notation
Sometimes we use SSS (side-side-side) to show that the corresponding triangles are congruent.

Example
△ABC\triangle ABC△ABC has side lengths AB=5cmAB=5 cmAB=5cm, BC=7cmBC=7cmBC=7cm and CA=3cmCA=3cmCA=3cm.
△XYZ\triangle XYZ△XYZ has side lengths XY=3cmXY=3cmXY=3cm, YZ=7cmYZ=7cmYZ=7cm and ZX=5cmZX=5cmZX=5cm.
Which two triangles are congruent?

△ABC≅△XZY\triangle ABC \cong \triangle XZY△ABC≅△XZY (by SSS)

Practice: Congruent Triangles
Suppose that △RST≅△DEF\triangle RST\cong \triangle DEF△RST≅△DEF. IfRS=6mRS=6mRS=6m, ST=7mST=7mST=7m and RT=10mRT=10mRT=10m, find the length of FDFDFD.

Enter the length of

FD

m

, do not include units.

I don't know

Practice: Congruent Triangles
△ABC\triangle ABC△ABC is a right angle triangle where ∠B=90°\angle B=90\degree∠B=90°, AB=3mAB=3mAB=3m, and BC=4mBC=4mBC=4m. If △ABC≅△XYZ\triangle ABC \cong \triangle XYZ△ABC≅△XYZ, determine the length of XZXZXZ.

Enter the length of

XZ

m

, do not include units

I don't know