Congruent Triangles Day 1 Objective Discover shortcuts for

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

A building contractor has just assembled two massive triangular trusses to support the roof of a recreation hall. Before the crane hoists 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?

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

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

Side-Side (SSS) 1. Construct triangle ∆ABC on tracing paper by using the parts from page 220. 2. Compare with your person on either side of you. Do you have identical triangles? SSS Congruence Conjecture If the three sides of one triangle are congruent to the three the triangles are congruent sides of another triangle, then ___________.

Side-Angle-Side (SAS) 1. Construct triangle ∆DEF on tracing paper from the parts on page 221 2. Compare with your person on either side of you. Do you have identical triangles? SAS Congruence Conjecture If two sides and the included angle of one triangle are congruent to two sides and the included angle of another, then ____________. the triangles are congruent.

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

Congruent Triangles Day 2 Objective: Discover shortcuts for determining congruent triangles

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

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

Angle-Side-Angle (ASA) 1. Construct triangle ∆MAT on tracing paper by using the parts from page 225. 2. Compare with your person on either side of you. Do you have identical triangles? 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 (SAA) is too short is too long is just right

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

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