Color-Coded Triangle Congruence Proofs Scaffolded Geometry Adapted Work (preview: 3 of 16 pages)

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Printing from a computer gives the most control over paper size and margins.

Triangle Congruence Proofs

Scaffolded Geometry Adapted Work Pack

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Visual Proof Reference Guide

Core Congruence Postulates & Properties

Geometric proof requires establishing that corresponding pairs of sides and angles are congruent. To assist visual organization, corresponding sides are color-coded in warm hues while corresponding angles appear in cool tones. The Side-Side-Side (SSS) Postulate states that if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. The Side-Angle-Side (SAS) Postulate requires two sides and the included angle—the angle formed directly between the two marked sides. The Angle-Side-Angle (ASA) Postulate requires two angles and the included side directly between them. When working with shared boundaries, apply the Reflexive Property of Congruence. Vertical angles formed by intersecting lines are always congruent.

SSS Postulate

SAS Postulate

ASA Postulate

Reflexive Property

Explain how the included angle in SAS differs fundamentally from a non-included angle.

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SSS Proof Guided Practice

Side-Side-Side Congruence

When three pairs of corresponding sides are confirmed congruent, triangles are congruent by the SSS Postulate. Shared segments between two adjacent triangles are congruent to themselves by the Reflexive Property. Use the bank to complete each statement or geometric reason.

Complete the statements and justifications for the scaffolded SSS congruence problems below.

1. Given that Segment AB ≅ Segment DE and Segment BC ≅ Segment EF, we need a 3rd side pair: Segment AC ≅ ____.

2. When two triangles share the identical boundary segment BD, the reason Segment BD ≅ Segment BD is the ____ Property.

3. If all three corresponding side pairs of ΔJKL and ΔPQR are congruent, which theorem justifies ΔJKL ≅ ΔPQR?

A) SAS PostulateB) SSS PostulateC) ASA PostulateD) CPCTC

4. The SSS Postulate requires knowing the measures of at least two internal triangle angles.

TrueFalse

5. Point M is the midpoint of Segment AB. Therefore, Segment AM ≅ Segment MB by the definition of ____.

6. State the geometric property used when stating Segment XY is congruent to Segment XY.

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