Featuring ASA and AAS (angle-side-angle and angle-angle-side)

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Presentation transcript:

Featuring ASA and AAS (angle-side-angle and angle-angle-side) Congruent Triangles Featuring ASA and AAS (angle-side-angle and angle-angle-side)

Congruent Triangles Checklist for congruent triangles 3 sides congruent 3 angles congruent SSS (side-side-side postulate) SAS (side-angle-side postulate)

Congruent Triangles using ASA and AAS The angle-side-angle postulate. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Congruent Triangles using ASA and AAS How does order matter for this postulate? Does it matter which angle is listed first or last?

Congruent Triangles using ASA and AAS Can we use ASA to prove any of the triangles to the right are congruent? How would you write the congruency statement? Why can’t we use triangle TWA? Can we use ASA to prove the below triangles are congruent? If so, how would you write the congruency statement?

Congruent Triangles using ASA and AAS The angle-angle-side theorem. If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.

Congruent Triangles using ASA and AAS Are the triangles below congruent by AAS? How would you write the congruency statement? For the triangles to the right, can we use AAS to show they are congruent? What would the congruency statement look like?

Ways to prove triangles are congruent Brainstorm! Working in pairs, write down as many ways as you can think of to prove triangles are congruent. Ways to prove triangles are congruent

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, SAS or ASA postulates or the AAS theorem. If we use the ASA postulate what must we show are congruent? Two angles and one side in between them! If we use the AAS theorem what must we show are congruent? Two angles and any side not between the two angles!

Interactive congruency app http://illuminations.nctm.org/Activity.aspx?id=3504