Congruent vs Similar Shapes

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. 

​

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

​

​

​

​

​

​

​Congruent vs Similar Shapes

Drag and Drop

Two ​

Placeholder

are congruent when ​

Placeholder

and all matching angles are ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

shapes

all matching sides

congruent

Drag and Drop

Congruent means ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

identical in shape and size

same angles

scale factor

same angles

​Similarity vs Congruency

Subject | Subject

​

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

Dropdown

Similar shape always has their ​

Select answer

in ​

Select answer

. This proportion is called the ​

Select answer

.

Dropdown

Similar shapes have similar​

Select answer

, but their ​

Select answer

are different. A quantity called ​

Select answer

is used to determine the relationship between ​

Select answer

sides.

Drag and Drop

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

ABC <----> DEF

That means that...

Side AB corresponds to ​

Placeholder

Side BC corresponds to ​

Placeholder

Side CA corresponds to ​

Placeholder

Drag these tiles and drop them in the correct blank above

side DE

side EF

side FD

Drag and Drop

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

ABC <----> DEF

That means that...

Angle A ​

Placeholder

angle D​

Angle B is equal to ​

Placeholder

​

Placeholder

is equal to angle F

Drag these tiles and drop them in the correct blank above

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

​

Subject | Subject

Some text here about the topic of discussion

Fill in the Blanks

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

Dropdown

If the corresponding ​

Select answer

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

Select answer

, side BC = ​

Select answer

, and side CA = ​

Select answer

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

Select answer

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

Drag and Drop

If ​

Placeholder

are congruent under the condition SAS, then ​

Placeholder

are congruent and the corresponding ​

Placeholder

the sides are also congruent.

Drag these tiles and drop them in the correct blank above

two triangles

two corresponding sides

angles between