8th GradeOctober 5 – October 9

(Mon/Tues) What are we doing today?

• Unit 1 Lesson 11 – Congruent Polygons & Lesson 12 – Congruent Polygons

• Trying to take over the world.

• Assignment #3 will close on Tuesday at 3pm.

• REMINDER: You should be working in MATHia this week!

Brief Quiz Discussion

• All of the quizzes have been scored. However, they will not be posted until later in the week.

• When scored out of 10 points, the average score was a 4.2.

• Though I will not discuss every quiz in class, I do intend to discuss this one in detail on Friday.

• If you were absent on Friday, e-mail me about taking the quiz. If the quiz is not taken by Friday, you will need to wait until an opportunity to retake is given.

• If you were present and just didn’t turn it in, then you will have to wait until an opportunity to retake is given.

Learning Targets

• I can decide visually whether or not two figures are congruent.

• I can decide using rigid transformations whether or not two figures are congruent.

Review of Translation, Reflection, & RotationTRANSLATION REFLECTION ROTATION

Non-Mathematical Term “moved” or “slid” “mirrored” or “flipped” “turned”

Picture

Description All points are moved direction & distance.

Each point and its image are the same distance

from the line of reflection

Each point and its image is the same distance from

the center of rotation

What do I look for? Figure and its image have same shape & orientation

but image is moved to another location.

Figure and its image show symmetry and appear as

mirror images

Figure and its image do not have same

orientation.

Information Needed direction (up, down, left, right) and distance (in

units)

line of symmetry direction (clockwise or counterclockwise), angle,

center of rotation

Rigid Transformations

• Rigid transformations do notchange any measurements (lengths or angles) of the original figure to create the image.

• Translations, rotations, and reflections are all rigid transformations.

• In 7th grade, we learned about scaled copies. If we use a scale factor other than 1, these transformations are not rigid transformations.

Congruent

• Congruent means two figures are the same shape and size.

• If you want to think of it physically, you could cut the figures out, put one on top of the other, and they would be a perfect match.

• If two figures are congruent, you can describe a series of rigid transformations to move one to fit exactly on the other.

• Note: The ≅ symbol means congruent. For example, Triangle A ≅ Triangle B reads “Triangle A is congruent to Triangle B”.

Exercise 12.2

• Are these figures congruent? Why or why not?

Exercise 12.2

• Are these figures congruent? Why or why not?

• These figures are congruent. If we reflect (flip) one of them to face the same direction as the other, we could then translate (move) them to be exactly on top of each other.

Exercise 12.2

• Are these figures congruent? Why or why not?

Exercise 12.2

• Are these figures congruent? Why or why not?

• These figures are not congruent. Notice how they are not exactly the same shape or size. For example, the side EA is 3 units in length. No side in the other figure is that long.

Exercise 12.2

• Are these figures congruent? Why or why not?

Exercise 12.2

• Are these figures congruent? Why or why not?

• These figures are congruent. Again, we could reflect (flip) one so that they face the same direction. Then, we would just need to translate (move) them to be in the same position. The sides all have the same lengths.

Exercise 12.2

• Are these figures congruent? Why or why not?

Exercise 12.2

• Are these figures congruent? Why or why not?

• These figures are not congruent. They are the same shape and have the same angles. However, they are not the same size. For example, compare the corresponding sides FE and NM. FE appears to be almost exactly 2 units. NM is not 2 units.

Practice Problems (#2 Only)

• Are these figures congruent? Why or why not?

(Wed/Thurs) What are we doing today?

• Unit 1 Lesson 13 – Congruence

• Trying to take over the world.

• REMINDER: You should be working in MATHia this week!

• REMINDER #2: If you were absent and did not compete QUIZ #1, you need to e-mail me to have it done by the end of the school today.

Learning Targets

• I can use distances between points to decide if two figures are congruent.

Activity 13.1

Activity 13.1 – Solution (Part 1 & 2)

• Notice how the distances between the corresponding points stays the same. For example, E to G is 2 units. Thus, E’ to G’ is also 2 units.

• If I placed Trapezoid ABCD onto Trapezoid A’B’C’D’ each corresponding set of points (i.e. A and A’, B and B’) would be on top of each other.

Activity 13.2

Activity 13.2 (Solution)

• Compare the distances inside of these ovals. Notice how the top ovals have identical dimension (though different orientations). They are congruent.

• Similarly, the bottom ovals are congruent (though measurements are not shown here).

Activity 13.4

Activity 13.4 (Solution)

• No, these are not congruent. Look at the distance between the eyes. On the left, the eyes are much closer together.

• Similarly the right side of the mouth is closer to the eyes in the image on the left.

Summary

• To be congruent, two figures must (1) be the same exact shape including having the same number of sides and the same measurements of all angles AND (2) be the same exact size including the same lengths of all sides.

• To show congruence, you can describe (generally) a series of rigid transformations (including translation, reflection, and rotation) which would move one of the figures to the position of the other figure.

• To show two figures are not congruent, you can show that they are not the same size OR not the same shape. For example, you could compare the lengths of sides or the measurements of angles.

Practice Problems (#1 – 4)

• If you do not have a book, you can access the problems online.

• https://access.openupresources.org/curricula/our6-8math/en/grade-8/unit-1/lesson-13/index.html

• Though I do not plan to grade this, some of you are tempting me to be evil by not working on practicing concepts discussed in class.

(Fri) What are we doing today?

• Review Quiz #1

• Trying to take over the world.

• Reminder: If you have not started in MATHia, you are giving up free points (which is bad).