Similar Vs. Congruent Figures

Similar Vs. Congruent Figures

Important Vocabulary

Similar: One figure is similar to another if there is a sequence of rigid transformations and dilations that moves the first figure so that it fits exactly
over the second.

Proportional: Relationships between two variables where their ratios are equivalent.

Corresponding: The parts of the original that match up to the image. The corresponding sides, angles, and points are in the same relative position.

Similar Figures

● Similar Figures have the same shape, but not the same size.

●They must have the same ratio of side lengths which is also called
proportional side lengths.

Multiple Choice

Sides in similar figures must be proportional.  

• True
• False 

Multiple Choice

All angles in similar figures are congruent.  

• True
• False

Multiple Choice

Are the following similar? Why or why not?

• Yes. All pairs of corresponding angles are congruent.
• No, the corresponding angles are not equal.
• No, the ratios of the corresponding sides are not equal.

Congruent Figures

• Congruent figures have the same shape and the same size

Multiple Choice

Tell whether the two figures are congruent.

• Yes, same size and same shape
• No, same shape but different sizes
• No, different size and different shapes

Multiple Choice

Are these two shapes congruent or not congruent?

• congruent
• not congruent

Multiple Choice

Translations, Rotations, and Reflections will always result in a figure that is _______ to the original.

• Congruent
• Bigger
• Smaller
• Similar

Multiple Choice

Dilations that change the size will result in a figure that is _______ to the original.

• Congruent
• Bigger
• Smaller
• Similar

Multiple Choice

If we are dilating a figure with a scale factor of 1, the image will be....

• Congruent
• Bigger
• Smaller

Congruent:
All corresponding side lengths
AND angle measures are the
same

Similar:
All corresponding angles are the same BUT the side lengths are not because our size is different

• The symbol means that the shapes are

similar

• The symbol means that the shapes are

congruent

The two triangles below are similar, determine the length of side x.

Example: Finding the length
of a Side of Similar Triangles

Example: Continued

Multiple Choice

Are the following similar? Why or why not?

• Yes
• No, the corresponding angles are not equal.
• No, the sides are not proportional.

Multiple Choice

Tell whether the two figures are similar. Explain your reasoning.

• Yes, similar because they are the same shape and side lengths are proportional.
• No, not similar because they are the same shape, but side lengths are not proportional.
• No, different sizes

Multiple Select

Congruent shapes have the same...

• Size

• Color

• Shape

• Rotation

Multiple Choice

Two shapes that are congruent are also similar

• False
• True

Multiple Choice

Two shapes that are similar are also congruent

• True
• False

Multiple Choice

Which angle corresponds with  $$\angle T$$  ?

• $$\angle U$$  

• $$\angle Q$$  

• $$\angle P$$  

• $$\angle R$$  

Multiple Choice

$$\Delta PQR\ is\ similar\ to\ \Delta STU$$  What side corresponds to side UT?

• PQ

• RQ

• QR

• QP

Multiple Choice

Find the height of the tree.

• 8 ft
• 12 ft
• 13 ft
• 15 ft

Multiple Choice

Solve for X.

• 2 ft
• 3 ft
• 4 ft
• 6 ft

Multiple Choice

Sides that are in the same position on two different figures are called...

• Corresponding Sides
• Corresponding Angles
• The Same
• Congruent Sides

Multiple Choice

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree.  How tall is the tree?

• 144 feet
• 72 feet
• 36 feet

Multiple Choice

Angles in the same position on two different figures are called...

• Corresponding Sides
• Corresponding Angles
• The Same
• Congruent Angles

Multiple Choice

What side is corresponding to line EF?

• BC

• ED

• EF

• AB

Multiple Choice

What side is corresponding to line AB?

• DE

• EF

• BC

• DF

Multiple Choice

What angle is corresponding to angle D?

• A

• B

• C

• F

Multiple Choice

The polygons are similar. Find x.

• 3

• 6

• 1.5

• 12

Multiple Choice

Are the two figures similar

• yes

• no

Multiple Choice

Find missing side

• 5
• 7
• 9
• 11

Multiple Choice

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

• x = 12
• x = 3
• x = 40
• x = 4

Multiple Choice

Two objects that are the same shape but not the same size are _______.

• Congruent
• Vertical
• Similar
• Complementary