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Congruent Triangles Day 1

Congruent Triangles Day 1. Objective: Discover shortcuts for determining congruent triangles.

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Congruent Triangles Day 1

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  1. Congruent TrianglesDay 1 Objective: Discover shortcuts for determining congruent triangles

  2. A building contractor has just assembled two massive triangular trusses to support the roof of a recreation hall. Before the crane hoists the them into place, the contractor needs to verify the two triangular trusses are identical. Must the contractor measure and compare all six parts of both triangles?

  3. What is the smallest number of parts needed? No Two? One? No Angle - Angle Angle Angle - Side Side Side - Side

  4. Three Parts? Side-Angle-Side (SAS) Side-Side-Side (SSS) Angle-Side-Angle (ASA) Side-Angle-Angle (SAA) Side-Side-Angle (SSA) Angle-Angle-Angle (AAA)

  5. Construct triangle ∆ABC on tracing paper by using the parts from page 220. • Compare with your person on either side of you.Do you have identical triangles? Side-Side-Side (SSS) If the three sides of one triangle are congruent to the three sides of another triangle, then ______________________. SSS Congruence Conjecture the triangles are congruent

  6. Construct triangle ∆DEF on tracing paper from the parts on page 221 • Compare with your person on either side of you.Do you have identical triangles? Side-Angle-Side (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another, then ________________________. SAS Congruence Conjecture the triangles are congruent.

  7. Congruencies that work: Side-Side-Side (SSS) Side-Side-Angle (SSA) Side-Angle-Side (SAS) B ∆BAD ∆BAT p. T D A

  8. Congruent TrianglesDay 2 Objective: Discover shortcuts for determining congruent triangles

  9. What works and what doesn’t? Side-Angle-Side (SAS) Side-Side-Side (SSS) YES YES Angle-Side-Angle (ASA) Side-Angle-Angle (SAA) Side-Side-Angle (SSA) Angle-Angle-Angle (AAA) NO

  10. Angle-Angle-Angle (AAA) Is this statement true? ∆MNO ∆PQR

  11. Angle-Side-Angle (ASA) • Construct triangle ∆MAT on tracing paper by using the parts from page 225. • Compare with your person on either side of you.Do you have identical triangles? If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then ___________________________. ASA Congruence Conjecture the triangles are congruent.

  12. Side-Angle-Angle (SAA) is too long is just right is too short

  13. Statement Reason Side-Angle-Angle (SAA) Given Deductive Reasoning Given B Given C Third angle Conjecture A Y ASA Conjecture ∆ABC ∆XYZ Z X If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle then __________________________. SAA Conjecture the triangles are congruent.

  14. p. What works and what doesn’t? Side-Angle-Side (SAS) Side-Side-Side (SSS) YES YES Angle-Side-Angle (ASA) Side-Angle-Angle (SAA) YES YES Side-Side-Angle (SSA) Angle-Angle-Angle (AAA) NO NO

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