Polygons and Congruent Figures

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.

Open Ended

Which one doesn't belong. EXPLAIN!

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 _______.

Open Ended

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

Line segment XY measures _______.

Determining which sides and angles correspond...

• Step one: Stack the names (if they are given)

•  $\frac{ABC}{XYZ}$  

• Look at which letters match up.

Multiple Choice

Which side corresponds with

 $\overline{AC}$ ?

•  $\overline{YZ}$  

•  $\overline{AB}$  
  

•  $\overline{XY}$  
  

•  $\overline{XZ}$  
  

Take a look at this video

https://www.youtube.com/watch?v=ip-xRWBa8M0&feature=youtu.be

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?