Download Triangle Congruence Theorems - Waukee Community School

Name:_____________________
Date:__________
Triangle Congruence Theorems
Illuminations Simulation Activity at: http://illuminations.nctm.org/ActivityDetail.aspx?ID=4
Exercise 1: If all three sides of one triangle have the same measure as the three sides of
another triangle, are the two triangles congruent?
 First choose 3 sides (click the boxes for sides AB, BC and AC)
 Match up vertices (pair the “B” from one segment to the “B” from another segment”).
 Once the vertices snap together, grab the end of a line segment and rotate it around.
 Snap together all three segments until they form a triangle.
 Three more segments will appear. These line segments all have the exact same length
as the three you started with. Snap these three together to form a triangle.
 Once you have two triangles, you can place them on top of each other- you can rotate
the triangles until they match. You can also flip them over with the “flip” button.
 Decide if the two triangles are congruent.
 Answer the question at the bottom of the screen.
 Try making one more triangle with the three segments. Try to make this one different
from the first two.
Answer this question: Is it possible to make 2 non-identical triangles if all the side
lengths have the same measure?
SSS Postulate (Side-Side-Side)
Complete this sentence: If all three sides of one triangle have the same measure as
the three sides of another triangle then:_________________________________________________
Exercise 2: If all three angles of one triangle have the same measure as the three angles of
another triangle, are the two triangles congruent?
 Choose 3 angles.
 Rotate them until they snap into a triangle
 Try it again with three of the same angle measures (they’ll automatically pop up)
 Answer the question at the bottom of the screen.
Answer this question: Is it possible to make 2 non-identical triangles if all the angles
have the same measure?
Answer this question: Should there be an AAA postulate?
Exercise 3: If two angles and the side in between them for one triangle have the same
measure as two angles and the side in between them of the other triangle, are the triangles
congruent?
 Click side “AB”, angle “A” and angle “B”
 Rotate the angles and match their vertices to the ends of the line segment until they all
snap into a triangle
 Do it again. Move the two triangles on top of each other and rotate or flip one of them
to see if the triangles are congruent
 Answer the questions at the bottom of the screen
 Try it again.
Answer this question: Is it possible to make 2 non-identical triangles if their
measurements for two angles and the side in between have the same measure?
ASA Postulate (Angle-Side-Angle)
Complete this sentence: If two angles and the side in between them for one triangle
have the same measure as two angles and the side in between them of the other
triangle then:___________________________________________________________________________
Exercise 4: If two angles and a side of one triangle have the same measure as two angles and
a side of the other triangle, are the triangles congruent?
 Click side “AB”, angle “A” and angle “C”
 Rotate angle A and match its vertex to the end of the line segment. Then try to place
angle C so that it creates a triangle with the other two parts.
 Do it again. Move the two triangles on top of each other and rotate or flip one of them
to see if the triangles are congruent
 Answer the questions at the bottom of the screen
 Try it again.
Answer this question: Is it possible to make 2 non-identical triangles if their
measurements for two angles and a side have the same measure?
AAS Postulate (Angle –Angle-Side)
Complete this sentence: If two angles and a side for one triangle have the same
measure as two angles and a side of the other triangle then:
___________________________________________________________________________
Exercise 5: If two sides and the angle between them of one triangle have the same measure
as two sides and the angle between them of the other triangle, are the triangles congruent?
 Click side “AB”, side “BC” and angle “B”
 Rotate and connect sides AB and BC to connect with angle B until the three pieces snap
into a triangle.
 Do it again. Move the two triangles on top of each other and rotate or flip one of them
to see if the triangles are congruent
 Answer the questions at the bottom of the screen
 Try it again.
Answer this question: Is it possible to make 2 non-identical triangles if their
measurements for two sides and the angle in between them have the same measure?
SAS Postulate (Side–Angle-Side)
Complete this sentence: If two sides and the angle between them of one triangle
have the same measure as two sides and the angle between them of the other triangle
then: ___________________________________________________________________________
Exercise 6: If two sides and the angle NOT between them of one triangle have the same
measure as two sides and the angle NOT between them of the other triangle, are the triangles
congruent?
 Click side “BC”, side “AC” and angle “B”
 Rotate and connect angle B onto side BC. Then connect AC onto side BC and try to
form a triangle
 Do it again. Move the two triangles on top of each other and rotate or flip one of them
to see if the triangles are congruent
 Answer the questions at the bottom of the screen
 Try it again.
Answer this question: Is it possible to make 2 non-identical triangles if their
measurements for two sides and the NOT angle in between them have the same
measure?
You will probably remember this for the rest of your life:
There is NO ASS in Geometry