Download Proving Triangles Congruent

Name____________________________
Date_____________
Proving Triangles Congruent
Congruent Sides
In this activity, you will examine whether S (side), SS (side-side) and/or SSS (side-side-side) guarantee
triangle congruence.
1. Under Conditions, select S.
a. Name the pair of sides in the triangles that are congruent. ________________
b. Drag the vertices of the triangles to form new triangles. Can you make triangles
that are not congruent? ________________________
c.
Click on Click to measure lengths and use the interactive rulers to measure the
lengths of AB and DE ; BC and EF ; AC and DF . Write the lengths here.
_______________________________________________________________
d.
Are all the pairs of sides always congruent?____________________________
e.
Does having one pair of sides congruent guarantee that two triangles are
congruent? Explain your answer. ___________________________________
_______________________________________________________________
2. Under Conditions, select SS.
a.
Name the pairs of sides in the triangles that are congruent. __________________
b.
Drag the vertices of the triangles to form new triangles. Can you make triangles
that are not congruent? ___________________________
c. Click on Click to measure lengths and use the interactive rulers to measure the
lengths of AB and DE ; BC and EF ; AC and DF . Write the lengths here.
_______________________________________________________________
d. Are all pairs of sides always congruent?_______________________________
e. Does having two pairs of sides congruent guarantee that two triangles are
congruent? Explain your answer. ______________________________________
___________________________________________________________________
3.
Under Conditions, select SSS.
a.
Name the pairs of sides in the triangles that are congruent. __________________
b.
Drag the vertices of the triangles to form new triangles. Can you make triangles
that are not congruent? ___________________________
c.
Click on Click to measure lengths and use the interactive rulers to measure the
length of AB and DE ; BC and EF ; AC and DF . Write the lengths here.
_______________________________________________________________
d. Are all pairs of sides always congruent? _______________________________
e. Does having three pairs of sides congruent guarantee that two triangles are
congruent? Explain your answer. ______________________________________
___________________________________________________________________
Congruent Sides and Angles
In this activity, you will examine whether the conditions SA (side-angle), SAS (side-angle-side), and/or
ASA (angle-side-angle) guarantee triangle congruence.
4. Under Conditions, select SA.
a.
Name the pair of sides and the pair of angles that are congruent. ______________
b.
What does adjacent mean? ____________________________________________
c.
Name another angle that is adjacent to each of the congruent sides. ___________
d.
Are those angles congruent? Click on Click to measure angles and use the interactive
protractors to measure the angles.
mA  _____; mD  ______; mB  ______; mE  ______; mC  ______; mF  _______
e.
Drag the vertices of the triangles to form new triangles. Can you make triangles
that are not congruent? __________________________________________
f.
Does having one pair of sides and a pair of adjacent angles congruent guarantee
congruent triangles? Explain your answer. ________________________________
___________________________________________________________________
5. Under Conditions, select SAS.
a.
Name the pairs of sides and the pair of angles that are congruent.
___________________________________________________________________
b.
In the top triangle, which angle is included between
and
? What is the
difference between adjacent and included?________________________________
___________________________________________________________________
c.
Drag the vertices of the triangles to form new triangles. Can you make triangles
that are not congruent? __________________________________________
d.
Does having two pair of sides and the corresponding pair of included angles
congruent guarantee congruent triangles always, sometimes or never? Explain
your answer. _______________________________________________________
___________________________________________________________________
6. Under Conditions, select ASA.
a.
Name the pair of sides and the pairs of angles that are congruent.
___________________________________________________________________
b.
Drag the vertices of the triangles to form new triangles. Can you make triangles
that are not congruent? _________________________________________
c.
Does having two pairs of angles and the corresponding pair of included sides
congruent guarantee congruent triangles always, sometimes or never? Explain
your answer. _______________________________________________________
__________________________________________________________________
Congruent Angles
In this activity, you will explore whether A (angle), AA (angle-angle), and/or AAA (angle-angle-angle)
guarantees triangle congruence.
7. Under Conditions, select A.
a. Name the pair of angles in the triangles that are congruent. ________________
b. Drag the vertices of the triangles to form new triangles. Can you make triangles
that are not congruent? ________________________
c.
Click on Click to measure angles and use the interactive protractors to find the
measures A of D and ; B and E ; C and F . Write the measures
here.
mA  _____; mD  ______; mB  ______; mE  ______; mC  ______; mF  _______
d.
Are all the pairs of angles always congruent? ___________________________
e.
Does having one pair of angles congruent guarantee that two triangles are
congruent? Explain your answer. ___________________________________
_______________________________________________________________
8. Under Conditions, select AA.
a.
Name the pairs of angles in the triangles that are congruent. __________________
b.
Drag the vertices of the triangles to form new triangles. Can you make triangles
that are not congruent? ___________________________
c.
Click on Click to measure lengths and use the interactive rulers to measure the
lengths of AB and DE ; BC and EF ; AC and DF . Write the lengths here.
_______________________________________________________________
d. Does having two pairs of angles congruent guarantee that two triangles are
congruent? Explain your answer. _______________________________________
__________________________________________________________________
e. If two pairs of angles are congruent, what can you conclude about the third pair
of angles?_________________________________________________________
9. Once you have tested AA (angle-angle) to see if it guarantees that two triangles are
congruent, there is no reason to test AAA (angle-angle-angle) because it is exactly the same
as AA. Explain why this is true. _________________________________________________
__________________________________________________________________________
__________________________________________________________________________
10. Which conditions CAN ALWAYS PROVE two triangles congruent? Circle your answers.
A
AA
AAA
S
SS
SSS
SA
SAS
ASA
SAA
SSA