8.1-8.4 review

Polygons and Congruent Figures

What are we doing today?

SOL 6.9

• Learning Intention: Today I will be able to determine the congruence of segments, angles, and polygons.

• Success Criteria: Today I will be successful when I can determine the congruence of segments, angles, and polygons correctly on at least 7 out of 10 practice problems.

ESSENTIAL QUESTION & UNDERSTANDING

• Essential Questions: Can looks be deceiving? If two things look alike, does that mean they are alike? 

• How do classification systems help us to understand the relationships between things? What are some classification systems that we regularly encounter? And can something belong to more than one group?

• Understanding: Congruent figures have the exact same size and shape.

• Any figure that has the attributes of more than one subset can belong to more than one subset. With geometry, things can look the same (or similar) but actually be different.

Vocabulary

• Congruent figures have exactly the same size and the same shape. 

• Line segments are congruent if they have the same length. 

• Angles are congruent if they have the same measure. 

• Congruent polygons have an en equal number of sides, and all the corresponding sides and angles are congruent.

Multiple Choice

Congruent figures have...

• the same number of sides

• the same shape, but different sizes

• the same shape and size

• are different shapes

More Vocabulary

• A regular polygon has congruent sides and congruent interior angles.

More Vocabulary

• Polygon classifications: 

  triangle (3 sides) quadrilateral (4 sides) pentagon (5 sides) hexagon (6 sides) heptagon (7 sides) octagon (8 sides) nonagon (9 sides) decagon (10 sides) dodecagon (12 sides)

Multiple Choice

Mrs. Turner has a painting with an area of 144 square inches. Which figure is congruent to her painting?

• A

• B

• C

• D

Open Ended

If △ABC is congruent to △XYZ then complete following statement.

Line segment BC is congruent to line segment _______.

Determining which sides and angles correspond...

Multiple Choice

Which side corresponds with

$$\overline{AC}$$ ?

• $$\overline{YZ}$$  

• $$\overline{AB}$$  
  

• $$\overline{XY}$$  
  

• $$\overline{XZ}$$  
  

Multiple Choice

Figures CMJXT and PDNER are congruent.
Which line segment in figure PDNER must be
congruent to $$\overline{JX}$$ ? 

• $$\overline{NE}$$  

• $$\overline{CT}$$  

• $$\overline{PR}$$  

• $$\overline{DP}$$  

Multiple Choice

Figures CMJXT and PDNER are congruent.
Which line segment in figure PDNER must be
congruent to $$\overline{RE}$$ ? 

• $$\overline{JT}$$  

• $$\overline{TC}$$  

• $$\overline{TX}$$  

• $$\overline{MX}$$  

Multiple Select

Which shapes are congruent to the figure (more than one)?

Multiple Choice

Figure ABCD is shown.

Which polygon appears

congruent to figure ABCD?

Symmetry

By Matthew Johnson

​Identify and describe the line(s) of symmetry in two-dimensional shapes

6GM44

Symmetry- when an object looks the exact same on one side as the other. (mirror image)

Lines of Symmetry- a line that divides a shape into two congruent parts. (equal or same size parts)​

​

​Some text here about the topic of discussion.

Multiple Choice

What is symmetry?

• When an object looks exactly the same on one side as it does on the other

• a mirror image of half of an object

• not identical halves

Multiple Choice

Does this rectangle have a line of symmetry?

• Yes

• No

Multiple Choice

How many lines of symmetry does this rectangle have?

• 0

• 1

• 2

• 4

Multiple Choice

Does this arrow have a line of symmetry?

• Yes

• No

Multiple Choice

Which arrow is symmetrical?

• A

• B

• Both

• Neither

Multiple Choice

What is symmetry?

• When an object looks exactly the same on one side as it does on the other

• a mirror image of half of an object

• not identical halves

Multiple Choice

Does this triangle have a line of symmetry?

• Yes

• No

In a regular polygon, all sides are the same length; therefore, the number of sides determines the number of lines of symmetry.​

​

​Some text here about the topic of discussion.

Count the number of sides the object has. That's how many lines of symmetry the regular polygon will have!

Regular Polygons

Multiple Choice

How many lines of symmetry does this object have?

• 0

• 1

• 3

• 6

Multiple Choice

How many lines of symmetry in a square?

• 2

• 4

• 6

• 8

Multiple Choice

How many lines of symmetry in a pentagon?

• 4

• 5

• 6

• 7

Multiple Choice

How many lines of symmetry does this shape have?

• 4

• 2

• 1

• 0

Multiple Choice

How many lines of symmetry in a regular octagon?

• 1

• 6

• 10

• 8

Multiple Choice

How many lines of symmetry does this shape have?

• 5

• 0

• 4

• 1

Perimeter and Area Review

Multiple Choice

What does perimeter mean?

• the amount of space inside a shape
• the distance around the shape
• the amount of space inside a shape divided by two
• half the distance around a shape

Multiple Choice

What is the perimeter?

• 20

• 40

• 60

• 80

Multiple Choice

What is the perimeter of the rectangle? (Hint: top matches the bottom, left matches the right!)

• 14 feet

• 28 feet

• 48 feet

• 20 feet

Multiple Choice

Find the perimeter of the irregular shape

• 28m

• 21m

• 30m

• 32m

Multiple Choice

The perimeter of the shape is 31 feet. What is the length of the missing side?

• 3 feet

• 4 feet

• 5 feet

• 6 feet

Multiple Choice

Find the perimeter of the rectangle.

Remember to combine like terms!

• 16x + 20

• 8x + 10

• 80x

• 18x

Multiple Choice

What is the formula for finding area of a rectangle?

• $$A\ =\ length\cdot width$$

• $$A\ =\ length\ +\ width$$
  

• $$A\ =\ length\ \cdot4$$

• $$A=\ width\ \cdot width$$ Area = Width x Width

Multiple Choice

What is the area of this figure?

• 12 sq. cm

• 32 sq. cm

• 16 sq. cm

• 28 sq. cm

Multiple Choice

What is the area of a square with a length of 5 cm?

• 10 sq cm

• 25 sq cm

• 20 sq cm

• 5 sq cm

Multiple Choice

If a rectangle has an area of 18 sq inches, what would be the 

length  $$\cdot$$   width?

• $$3\cdot3$$  

• $$3\cdot6$$  
  

• $$6\cdot6$$  
  

• $$4\cdot18$$  
  

Multiple Choice

The area of a rectangle is 25 cm². What could the length and width of the rectangle?

• 6 cm and 4 cm

• 5 cm and 5 cm

• 10 cm and 15 cm

• 5 m and 5 m

Area of Triangles

How can you use the formula for the area of a parallelogram to find the area of a triangle?

The diagonal of a parallelogram divides it into two identical triangles.

The area of one triangle must be half the area of a parallelogram that has the same base and height.

Multiple Choice

What is the area of this triangle?

• 49 square feet

• 600 square feet

• 100 square feet

• 300 square feet

Multiple Choice

What is the area of this triangle?

• 216 square cm

• 200 square cm

• 108 square cm

• 180 square cm

Fill in the Blank

What is the area of a triangle with b = 20 in and height = 3 in?

Fill in the Blank