Triangle Congruence Exploration
Name _______________________
Using AngLegs
During this activity, you will compare combinations of sides and angles that may be used to prove two triangles are
congruent. You have been given a bag containing AngLegs that represent segments that can be used to form a triangle.
The measurements are as follows:
Orange: 5 cm
Yellow: 10 cm
Purple: 7.07 cm
Blue: 12.24 cm
Green: 8.66 cm
Red: 14.14 cm
1. Given: 3 side measures of 8.66 cm, 10 cm and 12.24
How many different triangles can you create? __________
Sketch and label your triangle(s):
What combination of sides and angles did you use? ________________________________________________
Was this combination of sides and angles enough to establish congruence? _____________________________
2. Given: 3 angle measures of 45◦,45◦,90◦
How many different triangles can you create? __________
Sketch and label your triangle(s):
What combination of sides and angles did you use? ________________________________________________
Was this combination of sides and angles enough to establish congruence? _____________________________
3. Given: 2 angle measures of 55◦ and 55◦ , and one included side measuring 14.14 cm
How many different triangles can you create? __________
Sketch and label your triangle(s):
What combination of sides and angles did you use? ________________________________________________
Was this combination of sides and angles enough to establish congruence? _____________________________
4. Given: 2 sides measuring 14.14 cm and 7.07 cm, and one included angle measuring 60◦
How many different triangles can you create? __________
Sketch and label your triangle(s):
What combination of sides and angles did you use? ________________________________________________
Was this combination of sides and angles enough to establish congruence? _____________________________
5. Given: 2 angles measuring 79◦ and 59◦, and one non-included side measuring 14.14 cm
How many different triangles can you create? __________
Sketch and label your triangle(s):
What combination of sides and angles did you use? ________________________________________________
Was this combination of sides and angles enough to establish congruence? _____________________________
6. Given: One triangle with side measures of 5 cm, 8.66 cm and 10 cm and
A second triangle with side measures of 5 cm, 5cm, and 8.66 cm.
What do the triangles have in common? _________________________________________________________
__________________________________________________________________________________________
Sketch and label your triangle(s):
What combination of sides and angles did you use? ________________________________________________
Was this combination of sides and angles enough to establish congruence? _____________________________
Right Triangle Congruence Exploration
7. Given: A hypotenuse with a measure of 12.24 cm and one leg measuring 10 cm.
How many different right triangles can you create? __________
Sketch and label your right triangle(s):
What combination of sides and angles did you use? ________________________________________________
Was this combination of sides and angles enough to establish congruence? _____________________________
8. Given: One hypotenuse measuring 8.66 cm, and one acute angle measuring 35◦
How many different right triangles can you create? __________
Sketch and label your right triangle(s):
What combination of sides and angles did you use? ________________________________________________
Was this combination of sides and angles enough to establish congruence? _____________________________
Recap:
What proves triangle congruence?
What does not prove triangle congruence?
Triangle Proof Flow Chart
Information:
Justification:
Conclusion:
S
or
A
~
or

S
or
A
S
or
A
By__________________________