Geometric Transformation Congruence

Module 5- Congruence

By Tanya Conchas

Draw

Find the 5 differences between the pictures

Last class....

Rigid Transformations

There are 3 rigid transformations: Reflection, Rotation, Translation

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After the rigid transformations, the OG shape and Image are the same shape, size, same everything.

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We say the two shapes are CONGRUENT​

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First, Some Vocabulary...

Congruence -In geometry, congruent means identical in shape and size. The figures will have the same side lengths and same angles​

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Let's test your understanding of the word congruent!​

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Multiple Choice

Are these figures Congruent or not congruent?

• Congruent

• Not Congruent

Multiple Choice

Are these figures congruent or not congruent?

• Congruent

• Not Congruent

Multiple Choice

Are these figures congruent or not congruent?

• Congruent

• Not Congruent

Multiple Choice

Are these figures congruent or not congruent?

• Congruent

• Not Congruent

Multiple Choice

If Triangle ABC is the original, what transformation occurred to give you triangle DEF?

• Translation

• Rotation

• Reflection

Properties of Congruent Figures​

Ways to show congruence...

2) Draw tick marks on sides and angles to state congruence!

​1) Look at the sides/angles and see which sides/angles match

Congruent Vertices & Order

This tells us

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Side A̅B̅ ≅ Side ̅E̅F̅

Side AB is congruent to Side EF

Side AB corresponds to Side EF​

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​(Make sure that your corners match. Order of

vertices (corners) matter!)​

Once we determine the triangles are congruent...

We write a congruence statement to say

two shapes are congruent

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Δ​ABC ≅ ∆FEG

​*Triangle ABC is congruent to Triangle FEG*

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(Make sure your vertices (corners) match when writing you​r congruence statement!)

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Fill in the Blank

Side AB from the triangle on the left is congruent to Side _____ on the second triangle.

(Make sure your corner match)

Fill in the Blank

Side AC from the triangle on the left is congruent to Side _____ on the second triangle.

(Make sure your corners match)

Fill in the Blank

Side BC from the triangle on the left is congruent to Side _____ on the second triangle.

(Make sure your corners match)

Draw

Mark the all corresponding sides

Draw

Mark the all corresponding angles

Multiple Choice

Our final congruence statement is $$\Delta ABC\cong$$  ?

• $$\Delta EFD$$  

• $$\Delta DFE$$  

• $$\Delta DEF$$  

• $$\Delta FDE$$  

Draw

Mark the all corresponding sides with tick marks

Draw

Mark the all corresponding sides with tick marks

Multiple Select

What transformation(s) do you do to Polygon GHJK to get the polygon on the right?

• Translation

• Rotation

• Reflection

Draw

Mark the Corresponding sides with tick marks

Multiple Choice

Our final congruence statement is $$\Delta GHJK\cong$$  ?

• $$\Delta STQR$$  

• $$\Delta QRST$$  

• $$\Delta RSTQ$$  

• $$\Delta TQRS$$  

Open Ended

In your own words, what does it mean for two shapes to be congruent?