Congruence In Triangles using: CPCTC, SSS, SAS, ASA, AAS, HL, HA, LL, and LA.

You want to compare two 30 room buildings. Wouldn't be great if they told you that should you find out that if the front door, and the hall are equal, then the two buildings are identical; saving you the trip to all the remaining 30 rooms in each? This is the same with triangles, if you have to determine if two of them are congruent, then you may compare just three corresponding parts in each to prove that they are congruent. You save comparing all three angles, and all three sides. A total of six parts.

Triangle congruence in this lesson is approached allowing you to see in animations and colors: What corresponding parts are congruent to prove the congruence. This is the bridge you were looking for to start your connection to proofs with triangles!

Lesson's Content

Lesson's Glossary

Angle-angle-side (AAS) congruence states that if any two consecutive angles of a triangle are equal in measure to two consecutive angles of another triangle and a pair of corresponding not included sides to these angles is congruent; then the two triangles are congruent; that is, they have exactly the same shape and size.

Angle-side-angle (ASA) congruence states that if any two angles of a triangle are equal in measure to two angles of another triangle and the side in between each pair of angles have the same length, then the two triangles are congruent; that is, they have exactly the same shape and size.

Included angle
The angle made by two intersecting sides of a polygon.

Included side
The side between two consecutive angles in a polygon.

Side-angle-side (SAS) congruence states that if any two sides of a triangle are equal in length to two sides of another triangle and the angles between each pair of sides have the same measure, then the two triangles are congruent; that is, they have exactly the same shape and size.

The side-side-side (SSS) congruence states that if the three sides of one triangle have the same lengths as the three sides of another triangle, then the two triangles are congruent.

Interactive Geometric Applets: Relevant Theorems.

Drag point "B" to verify CPCTC. See how all corresponding parts remain congruent.

Drag point "B" and observe that the two known pairs of corresponding angles remain congruent, as

the non-included known side. This verifies Angle - Angle - Side

In this applet drag point "B" and check how the two corresponding angles and

the included corresponding side remain congruent.

This is a dynamic proof for Angle - Side - Angle.

Drag point "B" to confirm that Side - Angle - Side remains true for the two triangles.

Finally, in this applet you may confirm Side - Side - Side; for that drag point "B" like in the applets above.

Vocabulary Puzzle Interactive

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