Congruent TrianglesCongruent TrianglesDay 1Day 1

Objective:Objective:

Discover shortcuts for determining Discover shortcuts for determining congruent trianglescongruent triangles

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?

One? Two?

Angle - Angle

Angle - Side

Side - Side

What is the smallest number of parts needed?

Angle

Side

NoNo

Three Parts?Side-Angle-Side (SAS)Side-Side-Side (SSS)

Side-Angle-Angle (SAA)Angle-Side-Angle (ASA)

Side-Side-Angle (SSA) Angle-Angle-Angle (AAA)

If the three sides of one triangle are congruent to the three sides of another triangle, then ______________________.

SSS Congruence Conjecture

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?

Side-Side-Side (SSS)

the triangles are congruent

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

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?

Side-Angle-Side (SAS)

the triangles are congruent.

B

A

DT

∆BAD

Side-Side-Angle (SSA)

∆BAT

Congruencies that work:

Side-Side-Side (SSS)

Side-Angle-Side (SAS)

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Congruent TrianglesCongruent TrianglesDay 2Day 2

Objective:Objective:

Discover shortcuts for determining Discover shortcuts for determining congruent trianglescongruent triangles

What works and what doesn’t?Side-Angle-Side (SAS)Side-Side-Side (SSS)

Side-Angle-Angle (SAA)Angle-Side-Angle (ASA)

Side-Side-Angle (SSA) Angle-Angle-Angle (AAA)YES YES

NO

Angle-Angle-Angle (AAA)

∆MNO ∆PQR

Is this statement true?

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then ___________________________.

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

the triangles are congruent.

Side-Angle-Angle (SAA)

is too short is just rightis too longJK JKJK

If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle then __________________________.

Side-Angle-Angle (SAA)

Deductive Reasoning

ASA Conjecture∆ABC ∆XYZ

Third angle Conjecture

Given

Given

Given

ReasonStatement

SAA Conjecture

the triangles are congruent.

B

AC

Y

X Z

XA YB

ZC

YZBC

What works and what doesn’t?Side-Angle-Side (SAS)Side-Side-Side (SSS)

Side-Angle-Angle (SAA)Angle-Side-Angle (ASA)

Side-Side-Angle (SSA) Angle-Angle-Angle (AAA)YES YES

NO

YES YES

NO

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