Decomposing Polygons

Decomposing Congruent Shapes

By Colleen Whiting

If two shapes are congruent then that means they are the exact same size, and the exact same shape.​

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What does Congruent mean?​

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Draw

Draw an example of two shapes that are congruent!

Decompose means to break into smaller parts.​

When you decompose a shape you split a shape into smaller, equal parts.

Each part is labeled with a Unit Fraction.​

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What does it mean to Decompose a shape?​

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To write a Unit Fraction the numerator is always 1 and the denominator tells us how many parts the shape has. A Unit Fraction is one part of a whole.​

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1/2, 1/3, 1/5, 1/6 are all Unit Fractions​

Unit Fractions are used to label each part of a decomposed shape.​

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Let's look over a word problem together. Before we answer the question, lets identify the Unit Fractions that make up one part of the whole figure.​

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Multiple Choice

What is the Unit Fraction for one part of the whole figure?

• 3/4

• 4/4

• 1/4

• 4/1

Multiple Choice

Are the two shapes Congruent?

• Yes, they are congruent.

• No, they are not congruent.

​Now that we know each part is represented by 1/4 and both shapes are congruent, we can answer the question.​

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Multiple Choice

• F. Circle X Only

• G. Circle Y only

• H. Circles X and Y

• I. Neither Circle X or Y

How would you describe the shapes X, Y, and Z?​

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Turn and Talk.

Draw

Label each Unit Fraction.

​Now that we know the figures are congruent and all have the same unit fractions, let's solve the word problem.​ But wait, what does Equivalent mean?

Like congruent, equivalent fractions are when they are the same size and same shape, they take up the same amount of area.​

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Look at the examples to the right to get a better idea.

Equivalent means Equal.

Great! Now we know what equivalent means we can finally answer our word problem. Before you answer any problem make sure you know what each word means, and what your pictures represent.​

Multiple Choice

• O. Rhombus X

• P. Rhombus Y

• Q. Rhombus Z

• R. None. The shaded areas are equivalent.

Poll

How do you feel about Decomposing Congruent shapes now?

• Great! I can teach someone else!

• Good, i'm getting the hang of it!

• Okay, I might need some more help.

• I'm lost! Help!