Congruency statements and why triangles are congruent Congruent Triangles Congruency statements and why triangles are congruent

Why or How are triangles congruent What needs to be true about two triangles for them to be congruent Congruent – exactly the same Corresponding – same location in two figures, angle between congruent sides, right angle Assign groups to make specific types of triangles Sides Sides and Angle Angles and sides

Side Side Side If 3 sides of one triangle are congruent to 3 corresponding sides of another triangle then the triangles are congruent Construct a triangle with sides 2 in, 3 in and 4 in What do you notice about the triangles others created?

Side Angle Side Construct a triangle with an angle of 40 degrees and the two sides of the angle 3 and 4 inches What do you notice about the triangles of those around you? If two sides and the included angle of one triangle are congruent to two corresponding sides and the included angle of another triangle then the two triangles are congruent Included angle – angle between the two given sides

Angle Side Angle What do you think will be true if we construct a triangle knowing 2 angles and the side connecting them? If two angles and the included sides of one triangle are congruent to two angles and the included side of another triangle then the triangles are congruent Included side – side between the two given angles

Side Side Angle What do you think will happened when we construct a triangle with 2 sides and the angle not between them? This one does not work This spells a bad work backwards and we can’t use bad words in this class so it can’t be used

Shortcuts All of the statements that we have just learned help us to prove the triangles will be congruent. You saw this as you did the first two sets of constructions If we have enough information or markings on the triangles that is what helps us to determine if the triangles are congruent and why Basic idea of the proofs

Congruence Statement Remember corresponding parts of one triangle need to be in the same order as the second triangle Need triangle symbol in the front You could state congruent angles and sides of triangles just knowing the statement

Examples Why are the triangles congruent, or why not Finish the congruency statement

Homework Pg 224 4-9 and 12-17