Lesson Notes By Weeks and Term v4 - JHS 1

Lesson Video

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Performance objectives

• Define congruent and similar shapes.
• Identify congruent and similar shapes.
• Compare angles and sides to check for similarity.
• Find real-life examples of congruence and similarity.

Lesson summary

This lesson introduces two fundamental concepts in geometry: congruence and similarity. We see these ideas all around us in Ghana. When a tailor cuts multiple pieces of fabric for a dress using the same pattern, they are creating congruent shapes. When an artist sketches a small version of a large mural, or when we look at a map of our region, we are working with similar shapes. Understanding the difference helps us in design, construction, art, and even in understanding maps. Today, we will learn how to precisely define these terms and, more importantly, how to *prove* or *verify* if two shapes are congruent or similar by checking their properties.

Lesson notes

A. Congruent Shapes (≅)

What does "Congruent" mean? The word "congruent" is a formal way of saying "exactly the same". Two shapes are congruent if they have the same shape and the same size. Think of them as identical twins. If you can place one shape directly on top of the other so that it fits perfectly without any parts sticking out, then they are congruent. This might require you to slide (translate), turn (rotate), or flip (reflect) one of the shapes.

The symbol for congruence is ≅. So, if Triangle ABC is congruent to Triangle XYZ, we write ΔABC ≅ ΔXYZ.

How to Verify Congruence To prove that two polygons (shapes with straight sides) are congruent, you must check two conditions: All corresponding angles are equal. All corresponding sides are equal in length.