Geometry Congruent Figures

Having the same size and shape; ^≅.

• Congruent

• Similar

• Image

• Preimage

The pair of figures is similar. Find the missing side.

• x = 20

• x = 12

• x = 5

• x = 4

The pair of figures is similar. Find the missing side.

• x = 1

• x = 3

• x = 9

• x = 5

Solve for X.

• 2 ft

• 3 ft

• 4 ft

• 6 ft

Prove that figure ABC is congruent to figure XYZ. Fill in the blanks to complete the proof Segmnts AB and XY are the same length. Therefore there is a rigid motion that takes ​ AB to ​ ZY Apply that rigid motion to figure​ ABC . If, necessary, reflect the image of figure ​ ABC across ​ YZ to be sure the image of ​ C , which we wil call ​ C' is on the same side of ​ YZ as ​ X ​ (a)   must be on ray ​ (b)   since both ​ (c)   and ​ (d)   are on the same side of ​ (e)   and make the same angle with it at _____. Since points _____ and _____ are the same distance along the same ray from _____, they have to be in the same place. Therefore, figure ABC is congruent to figure XYZ.

• CB

• XY

• Y

• C'

• YX

• C

• X

• YZ

• B

• B'

Prove that figure ABC is congruent to figure XYZ. Fill in the blanks to complete the proof Segmnts AB and XY are the same length. Therefore there is a rigid motion that takes ​ AB to ​ ZY Apply that rigid motion to figure​ ABC . If, necessary, reflect the image of figure ​ ABC across ​ (a)   to be sure the image of ​ (b)   , which we wil call ​ (c)   is on the same side of ​ (d)   as ​ (e)   12 must be on ray ____ since both ______ and ______ are on the same side of ____ and make the same angle with it at _____. Since points _____ and _____ are the same distance along the same ray from _____, they have to be in the same place. Therefore, figure ABC is congruent to figure XYZ.

• XYZ

• CB

• YZ

• XY

• C

• C'

• X

• Y

​ Prove that figure ABC is congruent to figure XYZ.

Fill in the blanks to complete the proof

Segmnts AB and (a)   are the same length. Therefore there is a rigid motion that takes ​ (b)   to ​ (c)   Apply that rigid motion to figure​ (d)   .

If, necessary, reflect the image of figure ​ (e)   across ___ to be sure the image of ___, which we wil call ___ is on the same side of ____ as ____. 12 must be on ray ____ since both ______ and ______ are on the same side of ____ and make the same angle with it at _____.

Since points _____ and _____ are the same distance along the same ray from _____, they have to be in the same place.

Therefore, figure ABC is congruent to figure XYZ.

Blank 1

​ ​ ​ ​ ​ ​ ​ ​ ​

• XY

• AB

• ABC

• XYZ

• ZY

• CB

A transformation of a figure that flips the figure across a line.

• Reflection

• Translation

• Rotation

• Dilation

Solve the proportion:

• 15

• 5

• 10

• 12

Translate 1 unit down and reflect across the x-axis.

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