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Congruence
Chapter Two
Congruence
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Introduction
In fields like architecture, engineering and design, precise measurements and patterns Mathematics for Secondary Schools
are crucial. Maintaining such patterns and measurements across objects and designs
requires an understanding of the relationship between shapes and their properties. In
this chapter, you will learn about postulates, proofs and theorems on congruence as
well as the congruence of triangles. The competencies developed will enable you to
solve problems such as determining the dimensions of sides of figures without taking
actual measurements, designing and making objects of the same shapes and sizes such
as worn-out parts.
Think
Without knowledge of congruence industries would take longer time to
produce objects of the same shape and size.
The concept of congruence 3. Use real objects (e.g., coins or
The term congruence is derived from the books) to repeat task 1 (or 2 where
Latin word congruentia which means necessary) and compare your
agree or fit together exactly. Engage in observations.
Activity 2.1 to explore the characteristics
of objects from real life situations which In Activity 2.1, one may have noticed that
same objects matched exactly on top of
fit together.
each other. This means that the objects
have the same shape and size. Two or
Activity 2�1: Exploring congruence more objects with such characteristics are
of objects called congruent figures.
1. Create a shape of your choice in Postulates, theorems and proofs
Ms-Word, copy and paste it, then
drag it on top of the original and Understanding postulates, theorems, and
observe. proofs is important for developing a solid
2. Enlarge the original shape, overlap foundation in mathematics. These concepts
it with the copied shape, and note form the basis for logical reasoning and they
any changes. are used to validate mathematical ideas.
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