Triangle Shortcuts!!!.

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Presentation transcript:

Triangle Shortcuts!!!

In your groups… Open your textbook to pg. 222 and 223 In your group, complete the assigned Investigation. Each person needs to construct the triangle(s) as directed and compare the results. Be sure to thoroughly answer Step 3. You have 11 minutes to complete your Investigation.

Investigation 1: SSS Side Side Side (SSS) SSS Congruence Conjecture: If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent. Ask the group to explain before the slide. Ask the group to explain why. Ask for others to think of counterexample? If none, why not? If the sides are congruent, how do we know the angles are congruent? Is there are previous concept we have learned that helps prove this?

Investigation 2: SAS Side Angle Side (SAS) SAS Congruence Conjecture: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. **The angle must be adjacent to both sides!** Ask the group to explain before the slide. Ask the group to explain why. Ask for others to think of counterexample? If none, why not? Does the angle need to be between the two known sides, why or why not? Would this conjecture still hold true is the angle was not included between the two sides? Can you think of a counterexample?

Investigation 3: SSA Side Side Angle (SSA) SSA is NOT a triangle congruence shortcut. Counterexample: Ask the group to explain before the slide. Ask the group to explain why. Ask for others to think of counterexamples.

The Good, the Bad & the Ugly SSS and SAS: GOOD shortcuts SSA: Ugly (false) shortcut Do you think there are more GOOD shortcuts? Preview next lesson…

Angle Side Angle Angle Side Angle (ASA) ASA Congruence Conjecture: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Side Angle Angle Side Angle Angle (SAA) SAA Congruence Conjecture: If two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent.

Angle Angle Angle NOOO! AAA is NOT a triangle congruence shortcut. Counterexamples:

Good Bad SSS SSA SAS AAA ASA SAA