Exploring Triangle Congruence

Topic:Angles, Congruence, Geometry, Triangles

Corresponding Parts of Congruent Triangles are Congruent

When two triangles are congruent, this means that each angle and each side on one triangle has a corresponding angle or side on the other triangle that is congruent to the original. See if you can identify the corresponding pairs of angles and sides from the pair of congruent triangles below:

Two Congruent Triangles

Which side on triangle DEF corresponds with side AC?

Select all that apply

A
DF
B
DE
C
EF

Check my answer (3)

Which angle on triangle ABC corresponds with angle DEF?

Select all that apply

A
Angle ABC
B
Angle BCA
C
Angle CAB

Check my answer (3)

Do we really need all these pairs?

If two triangles are congruent, is true that EVERY pair of corresponding sides and angles are congruent... However, can we tell if two triangles are congruent without knowing information about all of the pairs? In each of the scenarios below, the two triangles share some amount of congruent features. By clicking and dragging the points, see if it is possible to create two NON-CONGRUENT triangles that still share those congruent features. HINT: Keep in mind that in GeoGebra, the measurements might not always be exactly the same. If two values are very similar, we can consider them to be equal.

S - Triangles share a single congruent side

SS - Triangles share two congruent sides

SSS - Triangles share three congruent sides

A - Triangles share one congruent angle

AA - Triangles share two congruent angles

AAA - Triangles share three congruent angles

SSA - Triangles share two congruent sides and a congruent angle not between them

Hint: Make sure the black of your triangle is lying along the red dotted line to ensure that the triangles share the congruent angle!

SAS - The triangles share two congruent sides and a congruent angle between the two sides

Hint: Make sure the blue and red sides line up with the green dotted lines to ensure that the triangles share the congruent angle!

ASA - Triangles share two congruent angles and a congruent side between those angles

Hint: Make sure the two black sides line up with the blue and green dotted lines to ensure that the triangles share the two congruent angles!

AAS - Triangles share two congruent angles and a congruent side not between those angles

Hint: Make sure the black lines on the triangles line up with the blue and red dotted lines to ensure that the triangles share the two congruent angles!