Download Congruence Powerpoint - Ms. Huls` Math Class

Happy Monday
Please do the following:
• Pick up the papers from the front table.
WARM-UP
Homework:
HW #2: Worksheet ( in class)
HW #3: Proof Practice
Extra Credit-Valentines Day Activity
Agenda
1. Group Posters
2. Intro to Congruent Triangles
Office Hours!
Everyday at lunch
Thursday= FLEX ( leaving at 3:15).
Learning Objective(s)
By the end of this period you will be able to:
① Use properties of congruent triangles
② Apply SSS and SAS to construct triangles and to solve problems
Feedback
Remember if you haven’t done so already, take
the survey and then email me the screenshot.
The link is on my website
Period 1- Did we do whiteboards?
Whiteboards
Grab a whiteboard!
Quick Check!
Name the included angle in each triangle.
G
I
H
Quick Check
1. If triangles are similar, what is true about
corresponding sides and angles?
1. If triangles are congruent, what is true about
corresponding sides and angles?
2. What is the difference between similarity and
congruence?
Triangle Congruence
Instead of having to prove that all sides and angles are congruent in
order to prove that triangles are congruent, we are going to learn 5
shortcuts.
There are five ways to prove triangles are congruent:
1. SSS
2. SAS
3. ASA
4. AAS
5. HL
Notes
Triangle Congruence Conjectures
Fill in the blanks as we go along. I will give you time to glue the paper
into your composition notebook.
We will go over Examples and Non-Examples. You may want to draw
more down in your notebook!
SSS and SAS
Side–Side–Side Congruence (SSS)
• If all three pairs of corresponding sides have equal length,
then ≅
What is a possible congruent statement for the figures?
• Examples
• Non-Examples
Side-Angle-Side Congruence
Side–Angle–Side Congruence (SAS)
• If two pairs of corresponding sides have equal length and
the angle in between them are equal, then ≅.
What is the possible congruence statement for the figures?
Example/ Non-Examples
• Example
• Non-Example
4-4 Triangle Congruence: SSS and
SAS
Angle–Side–Angle Congruence (ASA)
• If two angles and the side between them are congruent to
the corresponding angles and the side, then ≅
• What is a possible congruent statement for the figures?
ASA
• Examples
• Non-Examples
Angle-Angle-Side Congruence
Angle-Angle-Side(AAS)
• If two pairs of corresponding angles and a pair of
corresponding sides that are not between the angles have
equal measures, then ≅
What is the possible congruence statement for the figures?
Example/ Non-Examples: AAS
• Example
• Non-Example
Whiteboard!
On your whiteboard, draw a right triangle
1. Label the legs of the triangle
2. Label the hypotenuse
Hypotenuse-Leg (HL) Congruence
Hypotenuse-Leg Congruence (HL)
• If the hypotenuse and a leg of a right triangle are congruent
to the hypotenuse and a leg of another right triangle, then
the triangles are congruent.
• IMPORTANT: The hypotenuse is ALWAYS across from the
right angle ( highlight this in your notes)
Examples/Non-Examples: HL
• Example
• Non-Example
Math Joke of the Day
• What do you call a broken angle?
• A rectangle!
Whiteboards
Identify the postulate or theorem that proves the triangles
congruent.
HL
ASA
SAS or SSS
Whiteboard Flash!
I am going to show you two triangles
You are going to write down whether they are congruent by
SSS, SAS, AAS, ASA, or HL!
Once your entire table thinks they have it correct, STAND UP!
First table to have ALL their members stand up with the
correct statement wins that round.
Note: The triangles might not be congruent. If so, state they are not
congruent.
Flash Warm-Up!
I will show a picture and you will write on your
whiteboard what triangle congruence postulate
you should use to prove the triangles are
congruent.
Recall the possible postulates are:
1.
2.
3.
4.
SSS
SAS
ASA
AAS
(1)
(2)
Flash Do Now!
(2)
Flash Do Now!
(2)
Flash Do Now!
CHALLENGE: Flash Do Now!
(3)
Classwork #2
Homework #2
Kahoot!
①Only ONE person needs his/her phone
②Go to kahoot.it on your Safari browser ( or other
browser)
③Type in the game-pin that you see on the whiteboard
④Create a nickname for you and your partner ( MUST be
school appropriate)
⑤Is your name on the whiteboard?
⑥The question will appear on the whiteboard and then
you have to answer it on the phone! ( multiple choice).
You will see if you got it correct! It will keep score so I
can see who is the winning team! You will get a treat!
Classwork #3
Complete the front side.
When done, try to do the back. 2 column proofs
are very similar to flow chart proofs. They are
just organized in a different way.
Around the World
1. Open up your composition notebook to the next page and
title it Around the World.
2. I have posted around the room 4 questions on yellow
paper. You will go the question closest to your table and
copy down the problem into your notebook. Then you will
answer the question. Write down the letter that was on the
bottom of the yellow paper.
3. Once you get a solution you will go look around at the other
yellow papers and at the bottom of one of the papers
should be your solution. That is the next problem you will
attempt. Also write down the letter.
4. If you are successful, you should go to each question and
end up at the question you started at.
5. When done, you will have 4 letters and unscramble them to
make a word.
Around the World-Expectations
1. Show ALL work. Do not just copy your table-mates solutions
or the solutions on the whiteboard.
2. Help each other out.
3. No yelling and/or running.
4. I will give you 15 minutes for this activity.
5. When done, you will show MS. Huls all your work and she
will put your grade in Synergy at that time.
6. BE ON TASK!
HW #3
On Front:
• You are going to find my mistakes and fix them! I gave you a
hint on how many mistakes I made on each proof
On back:
• Write your own two-column proofs!!!
Posters
1. Pick a partner you want to work with
2. I am going to give you a proof and you are going to first
write it in your notebook. When done, raise your hand and I
will give you poster paper
3. On poster:
1. Draw the picture
2. Write a two-column proof
3. Write down what was hard about the proof ( was it
vertical angles, reflexive property, HL, etc? )
4. You and you partner are going to present your proof to the
class.
Valentine Activity: Extra Credit
• For extra credit you will be writing a letter to a
loved one. This loved one can be your parent,
sibling, or partner .
• Let’s brainstorm vocabulary words that we have
learned so far this year.
• You must use at least 10 vocab words. I will be
collecting this on Thursday/Friday.
• No late extra credit will be accepted.
• Can be typed and emailed to me or hand-written.
Examples
To my Valentine:
Our love is like an irrational equation; it can’t be
simplified.
You are a factor of my life.
If we distribute our love, we can be together forever.
Together, we make a perfect square.
I love you like a coefficient loves its variable.
You are the square to my root, the solution to all of my
equations. The slope of my love for you is ever
increasing.
We fit together like coordinates on an axis
Examples
Yesterday, I was passing by your rectangular
house in trigonometric lane. There I saw you
with your cute circular face, conical nose and
spherical eyes, standing in your triangular
garden.
Examples