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Understanding Inequalities in Triangles: Properties and Examples

This section delves into the properties of inequalities within triangles, providing clear examples to illustrate the concepts. Learn how to identify and circle the largest angles in triangles, as well as list angles and sides in order from smallest to largest. The examples guide you through sequentially ordering both sides and angles, enhancing comprehension of triangle properties. This foundational knowledge will strengthen your overall understanding of geometry and how angles relate to the sides of triangles.

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Understanding Inequalities in Triangles: Properties and Examples

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  1. Section 5.3 Inequalities in One Triangle Objective: Apply properties of inequalities.

  2. Example 1 Circle the largest angle. • <1, <2, <5 • <5, <7, <4 • <1, <2, <7 • <6, <3, <4

  3. Example 2 List the angles and sides in order from smallest to largest.

  4. Example 3 List the sides and angles in order from shortest to longest.

  5. Example 4 List the sides and angles of ∆ABC in order from shortest to longest.

  6. Example 5 Circle the largest. 1. m<QRW, m<RWQ 2. m<RTW, m<TWR 3. m<RST, m<TRS 4. m<WQR, m<QRW

  7. Example 6 Circle the largest. 1. DH, GH 2. DE, DG 3. EG, FG 4. DE, EG

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