UNIT OVERVIEW

This unit builds on your earlier work with congruent triangles and circle geometry. You will now learn how to work with similar figures — shapes that have the same form but different sizes.

In this unit, you will learn to:

• Identify when two polygons are similar
• Prove and apply the Basic Proportionality Theorem (also called the Triangle Proportionality Theorem)
• Understand the Midpoint Theorem as a special case of proportionality
• Prove that equiangular triangles are similar
• Prove that triangles with sides in proportion are similar
• Derive the Pythagorean Theorem using similarity
• Solve examination-style problems involving proportionality and similarity

Where you will use these skills:

• Scale drawings: Architects and engineers use similar shapes when making scale models of buildings or machines.
• Surveying: Land surveyors use similar triangles to measure distances across rivers or to tall structures.
• Shadow problems: You can calculate the height of a building by comparing its shadow to the shadow of an object with known height.

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