Congruent and Similar Shapes (3A)

In geometry, congruent means identical in shape and size. Congruence can be applied to line segments, angles, and figures. 

• Any two line segments are said to be congruent if they are equal in length. 

• Two angles are said to be congruent if they are of equal measure. 

• Two triangles are said to be congruent if their corresponding sides and angles are equal. 

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Important Points:

• The word 'congruent' means 'exactly equal' in terms of shape and size. 

• Congruence exists even when the shapes are oriented differently: turn, flip, or rotate

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​Congruent vs Similar Shapes

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Two ​

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are congruent when ​

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and all matching angles are ​

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.

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shapes

all matching sides

congruent

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Congruent means ​

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.

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identical in shape and size

same angles

scale factor

same angles

​Similarity vs Congruency

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​

Similarity:

1. Two shapes are similar if their corresponding sides have dimensions with a common ratio (called scale factor). 

2. Similar shape-

   • size is not preserved: Enlargement or reduction

   • the angle between the corresponding sides is preserved

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Similar shape always has their ​

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in ​

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. This proportion is called the ​

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.

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Similar shapes have similar​

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, but their ​

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are different. A quantity called ​

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is used to determine the relationship between ​

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sides.

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Given that triangle, ABC is similar to DEF. That is,

ABC <----> DEF

That means that...

Side AB corresponds to ​

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Side BC corresponds to ​

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Side CA corresponds to ​

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side DE

side EF

side FD

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Given that triangle, ABC is similar to DEF. That is,

ABC <----> DEF

That means that...

Angle A ​

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angle D​

Angle B is equal to ​

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​

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is equal to angle F

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equal to

angle D

Angle C

​Congruency

Two shapes are congruent if one shape can become another using

• Turns, 

• Flips and/or

• Slides 

Congruent shapes-

• size is preserved: same shape and size

• the angle between the corresponding sides is preserved

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Subject | Subject

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Fill in the Blank

Congruent images have the same _____.

Match

Match the following

• Same Shape

  Same Size

• Same Shape

  Different Size

• Angular Measurements are preserved

Congruent Images

Similar Images

Both Congruent and Similar images

• Congruent Images

• Similar Images

• Both Congruent and Similar images

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If the corresponding ​

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of triangle ABC and Triangle DEF are congruent, then side AB = ​

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, side BC = ​

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, and side CA = ​

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We can say that the two triangles are ​congruent under the condition ​

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Multiple Select

If the corresponding angles of two triangles are equal, then the triangle is congruent under the condition of Angle-Angle-Angle (AAA)

• True

• False

• Not necessarily

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If ​

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are congruent under the condition SAS, then ​

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are congruent and the corresponding ​

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the sides are also congruent.

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two triangles

two corresponding sides

angles between