Copy of Exploring Triangle Congruence
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?
Which angle on triangle ABC corresponds with angle DEF?
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
Is one congruent side enough to determine if two triangles are congruent? Tell me why or why not.
SS - Triangles share two congruent sides
Are 2 congruent sides enough to determine if two triangles are congruent? Tell me why or why not.
SSS - Triangles share three congruent sides
Are 3 congruent sides enough to determine if two triangles are congruent? Tell me why or why not.
A - Triangles share one congruent angle
Is one congruent angle enough to determine if two triangles are congruent? Tell me why or why not.
AA - Triangles share two congruent angles
Are 2 congruent angles enough to determine if two triangles are congruent? Tell me why or why not.
AAA - Triangles share three congruent angles
Are 3 congruent angles enough to determine if two triangles are congruent? Tell me why or why not.
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!
Are 2 congruent sides and a congruent non-included angle enough to determine if 2 triangles are congruent? Tell me why or why not.
(an included angle is an angle between two sides- a non-included angle would be one NOT between the two sides)
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!
Are 2 congruent sides and a congruent included angle enough to determine if 2 triangles are congruent? Tell me why or why not.
(an included angle is an angle between two sides- a non-included angle would be one NOT between the two sides)
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!
Are 2 congruent angles and a congruent included side enough to determine if 2 triangles are congruent? Tell me why or why not.
(an included side is a side between two angles- a non-included side would be one NOT between the two 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!
Are 2 congruent angles and a congruent non-included side enough to determine if 2 triangles are congruent? Tell me why or why not.
(an included side is a side between two angles- a non-included side would be one NOT between the two angles)