So far, we have learned two ways of showing triangles are congruent
Today we will add two more congruence relationships between trianglesWe will use triangle congruence worksheet with this lesson (ebackpack)
DefinitionAngle-angle-side (AAS) - Two triangles that have corresponding angles and a non-included side congruent are themselves congruent.
Note: What can you say about <A and <D in the diagram?
…Given two corresponding congruent angles in a set of triangles the third angle has to be congruent as well (which we can mark)
So…AAS in a way is an extension ASA.
State what you know and what you would need to find out in order to have AAS congruence.
Applying AAS #1Know:
Need to know:
Is there enough information to say that the triangles are congruent if there is, state what you know. If there is not state what else you would need to know.
Applying AAS #2
DefinitionSide-side-side congruence (SSS)- If all three sides are congruent and corresponding in two triangles then the triangles are congruent.
Congruence statement for the diagram:
∆ ______≅ ∆ ______
Can ∆VUW ≅ ∆MLN?
Check if all corresponding sides give you the same value for x:
Now answer #3 on the worksheet.
Why does SSA not work?1) Start with figure 3-A and extend
segment AC (figure 3-B).
2) Swing segment BC across until it touch the extension of segment AC (figure 3-C)
3) You have just created two triangles (3-A and 3-D) that have SSA ≅ but are not ≅
DefinitionHL congruence (HL) – If the hypotenuse and one of the legs in a right triangle are congruent to the hypotenuse and a leg in another triangle the triangles are congruent. This only works with right triangles!
Notice: Even though we have SSA, since we know the triangles are right, we can say that they are congruent because of HL.
Summary of showing triangle congruence: ASA SAS AAS SSS HL
Go through and with a neighbor (or by yourself) write what type of triangle congruence each diagram shows (if any).
Origami Japanese art of folding paper without cutting or gluing.
Few number of general folds can produce infinitely many designs