Welcome to your
This digital booklet is to help you practice and recognize the rules to knowing if triangles are congruent.
How to use this resource:
Read through to review what you learned in class
Compare examples to your homework
Practice figuring out which theorem you have
Sides have notches through the side of the triangle. Angles have arcs through the corners. Go the SHORTEST DISTANCE along the marked parts of the triangles.
If you went the long distance around this triangle, you might think it is SAS, which it is not
looking
What you’re looking for:
Three sets of sides marked congruent or two sets of sides marked with a shared side.
Why it works:
If all three sides of one triangle are the exact same of all three sides of a second triangle, they are identical, or congruent.
Sense: move on to the next page
No Sense: read page this again or ask for help
What you’re looking for: Hash marks, angle marks, then marks again going around a corner. A shared side is always a congruent side.
Think of the angle as a hinge. If the hinges are open to the exact same amount, and the sides on either side of the hinge are the exact same amount, then there’s only one possible option for the third side, meaning the triangles have to be congruent.
Sense: move on to the next page
No Sense: read page this again or ask for
What you’re looking for: Angle congruency arcs, a congruent side, and another set of angle marks along one side.
When the side enclosed by two angles are all congruent, there’s only one option for the other two sides to connect to make a triangle. If I told you to construct a triangle with a 85° angle, followed by a 5cm side, followed by a 35° angle all in a row, there is only one triangle you could make with those specifications.
Sense: move on to the next page
No Sense: read page this again or ask for help
What you’re looking for:
Two separate congruent angles and one of the sides not between them with a hash mark.
When you have two angles congruent, the third also has to be congruent. If you additionally know that one side is congruent, the other two have to be for all three angles to be the same. Or you can think about how once you know the third angle also works, this just turned into ASA.
Sense: move on to the next page
No Sense: read page this again
What you’re looking for:
A right triangle (triangle with a 90° angle) with the longest side and one of the two shorter sides congruent.
Why it works:
The Pythagorean Theorem! When you have a right triangle, if the hypotenuse and one leg are the same, the third side has to be the same. This is a special kind of SSS where you only need to prove two of the sides to know the third one works too.
Sense: move on to the next page
No Sense: read page this again
When you go in the actual shortest distance around the triangle, it spells a bad word!
LIES!
The angle between the two congruent sides could be anything. There are multiple triangles that could work with these specificactions.
SSA could either make the obtuse triangle or acute triangle
Sense: move on to the next page
No Sense: read page this again or ask for help
Two triangles who have no sides in common.
When all the angles are the same, it doesn’t mean the triangles are the same size. These two triangles are similar, however. (Something we will go over in the future.)
Sense: you’re done!
No Sense: read page this again or ask for help
