Congruent Triangles Featuring SSS and SAS (side-side-side and side-angle-side)

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Presentation transcript:

Congruent Triangles Featuring SSS and SAS (side-side-side and side-angle-side)

Congruent Triangles  Checklist for congruent triangles  3 sides congruent  3 angles congruent  We will now learn how to use our theorems and postulates to cut the list in half!

Congruent Triangles using SSS and SAS  The side-side-side postulate. If three sides of one triangle are congruent with three sides of another triangle, then the two triangles are congruent.

Congruent Triangles using SSS and SAS  What construction method have we used that is very similar to this?  How many different triangle configurations could you make by rearranging the sides?

Congruent Triangles using SSS and SAS  Think about this: if you divide a square by drawing a line along one diagonal, what have you created?  What do we know about the sides of a square?  What property allows us to say the diagonal is congruent with itself?  Do we have three sides congruent?  Will this process hold if we have a rectangle? Rhombus? As long as we have a figure with two congruent sides plus the diagonal, yes!

Using prior learning

Congruent Triangles using SSS and SAS  The side-angle-side postulate. If two sides and the included angle between those sides are congruent to the corresponding parts of another triangle, then those two triangles are congruent.

Congruent Triangles using SSS and SAS  The side-angle-side postulate. If two sides and the included angle between those sides are congruent to the corresponding parts of another triangle, then those two triangles are congruent.

Your turn!  Would you use SSS or SAS to prove the following triangles are congruent? Is there enough information to choose?  We can use SAS for these triangles because we have two congruent sides plus the angle between those sides.  We can NOT use SAS for these triangles because the angle in the second triangle is not between the two congruent sides.

Your turn!  Would you use SSS or SAS to prove the following triangles are congruent? Is there enough information to choose?  We can use SSS for these triangles because we have three congruent sides.  We can use either SSS or SAS for these because we have three congruent sides plus a congruent included angle between two of the congruent sides.

Using SSS and SAS in a proof  Complete the flow proof

Brainstorm!  Working in pairs, write down as many real life examples of congruent triangles that you can think of. Congruent Triangles

Summing it all up!  For triangles, we need to show that all three sides and all three angles are congruent unless we make use of the SSS and SAS postulates.  If we use the SSS postulate what must we show are congruent?  Three sides!  If we use the SAS postulate what must we show are congruent?  Two sides AND the angle included between the two sides!