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Learning Goal: IWBAT to solve for unknown angles in triangles by writing
geometric proofs.
Homework: HW 3.3B: Exterior Angle Theorem Worksheet
-------------------------------------------------------------------Do Now:
Suppose you had four straws with the given side lengths:
5cm, 7cm, 19cm, 13 cm
Which three straws will form a triangle? Why?
September 10, 20131) Sit. 2) Materials out. 3) Backpacks away. 4) Do Now SILENTLY.
Agenda:
1. Do Now (15 min)
2. Triangle Proofs Lecture (30 min)
3. Triangle Proofs Card Sorts (35 min)
4. Triangle Algebra Activity (35 min)
5. Closure (5 min)
Review Triangle Theorems
Triangle Proofs – Example 1
Given m∠ ABC = 30°
m∠ BCA = 20°
Prove m∠ DAE = 130°B
C
A E
D
Triangle Proofs – Example 2
Given m∠ EAB = 155°
m∠ ABC = 60°
Prove m∠ ACD = 85°B
C
A
E
D
Triangle Proofs – Example 3
Given m∠ RPQ = 30°
m∠ PQR = (4x+2)°
m∠ HRQ = (8+6x)°
Prove x = 12
Triangle Proofs Activity
You will work with the person sitting next to you. Each pair will receive paper cut-outs containing the steps of a geometric proof to a triangle problem.
Each geometric proof is color coded to make it easier for you to arrange the paper cut-outs.
Your task is to arrange the paper cut-outs into a two-column proof. Then copy the proof in your notes.
The teacher will ask certain pairs to present their geometric proof to the class.
Triangle Algebra Activity
Students break up into groups of 3 or 4. Groups have been predetermined. Each group receives a whiteboard, marker, and eraser.
Teacher will present practice exercises about triangles on the board.
Your teams have 2 minutes to solve the problem and write the answer on the whiteboard with its justification.
The correct answer receives 1 point. The correct justification receives an additional point.
Geometry Period 2 Teams Red Team
1. George O.
2. Mayra R.
3. Charles L.
4. Ashley T.
Green Team
1. Ben M.
2. Kathy M.
3. Christian V.
4. Brisya C. Blue Team
1. Jose L.
2. Carina A.
3. Jackie D.
4. Diana O.
Yellow Team
1. Oscar E.
2. Jazmin A.
3. Nancy L.
4. Miguel B.
Purple Team
1. Linda
2. Jovanny H.
3. Adolfo G.
4. Justlene S. Orange Team
1. Ben L.
2. Susana A.
3. Abel
Geometry Period 4 Teams Red Team
1. Dennise P.
2. Amanda V.
3. Seth F.
4. Javier G.
Green Team
1. Veronica S.
2. Arthur D.
3. Lorena G.
4. Alfonso M.
Blue Team
1. Angie Z.
2. Miranda D.
3. Sydney G.
4. Oscar S.
Yellow Team
1. Jesus R.
2. Ariana P.
3. Leslie V.
4. Erick M.
Purple Team
1. James L.
2. Lee Ann Q.
3. Mirna A.
4. Thea Q. Orange Team
1. Christina G.
2. Derek A.
3. Yuleni V.
Geometry Period 6 Teams Red Team
1. Freddy A.
2. Anthony S.
3. Hannya O.
4. Ashley L.
Green Team
1. Christina R.
2. Geovanni B.
3. Oscar G.
4. Sabrina L. Blue Team
1. Jose S.
2. Jailene L.
3. Abigail G.
4. Andy H.
Yellow Team
1. Paulina C.
2. Martin R.
3. Melissa R.
4. Jonathan T.
Purple Team
1. Alexis A.
2. Deborah H.
3. Sabrina O.
4. Cristian B. Orange Team
1. Steven P.
2. Wendy G.
3. Leslie H.
Exercise #1
Find the measure of the unknown angle shown below.
Exercise #2
Find the measure of the unknown angle shown below.
Exercise #3
Find the measure of the unknown angle shown below.
Exercise #4
Find the measure of the unknown angle shown below.
Exercise #5
Find the value of x shown below.
Exercise #6
Find the value of x shown below.
Exercise #7
Find the value of x shown below.
Exercise #8
Find the value of x shown below.
Exercise #9
Exercise #10
Exterior Angle Theorem Masters Period 1
1. .
2. .
3. .
4. .
Period 2
1. .
2. .
3. .
Period 4
1. .
2. .
3. .
4. .
Period 5
Period 3
1. .
2. .
3. .
4. . Period 6
1. Jose S.
2. Andy H.
3. Abigail.
4. .
Triangle Algebra Activity
Students break up into groups of 3 or 4. Groups have been predetermined. Each group receives a whiteboard, marker, and eraser.
Teacher will present practice exercises about triangles on the board.
Your teams have 2 minutes to solve the problem and write the answer on the whiteboard with its justification.
The correct answer receives 1 point. The correct justification receives an additional point.
Geometry Period 1 Teams Red Team
1. Florian S.
2. Lupe V.
3. Ana G.
4. Julyssa M.
Green Team
1. Kharla P.
2. Norma R.
3. George M.
4. Kate V. Blue Team
1. Alejandra P.
2. Evelyn C.
3. Mario L.
4. Monica G.
Yellow Team
1. Kenny C.
2. Jessica D.
3. Steven F.
4. Ashley S.
Purple Team
1. Juda M.
2. Daniel P.
3. Lawrie S.
4. Jennifer B. Orange Team
1. Rene M.
2. Susana F.
3. Lizette M.
4. Ashley V.
Geometry Period 2 Teams Red Team
1. George O.
2. Mayra R.
3. Charles L.
4. Ashley T.
Green Team
1. Ben M.
2. Kathy M.
3. Christian V.
4. Brisya C. Blue Team
1. Jose L.
2. Carina A.
3. Jackie D.
4. Miguel B.
Yellow Team
1. Oscar E.
2. Jazmin A.
3. Nancy L.
Purple Team
1. Linda
2. Jovanny H.
3. Adolfo G.
4. Justlene S. Orange Team
1. Ben L.
2. Susana A.
3. Abel P.
Geometry Period 3 Teams Red Team
1. Alexis A.
2. Nathone G.
3. Kimberly M.
4. June M.
Green Team
1. Silver H.
2. Christian D.
3. Raquel P.
4. Julio Q.
Blue Team
1. Stephanie S.
2. Alanis G.
3. Daniel T.
4. Alice S.
Yellow Team
1. Anika G.
2. Sarah J.
3. Matthew D.
4. Andrea Q.
Purple Team
1. Stephanie L.
2. Adrian D.
3. Armando H.
4. Karla L. Orange Team
1. Erica C.
2. Jose S.
3. Jorge A.
4. Kate R.
Geometry Period 4 Teams Red Team
1. Dennise P.
2. Amanda V.
3. Seth F.
4. Javier G.
Green Team
1. Veronica S.
2. Arthur D.
3. Lorena G.
4. Alfonso M.
Blue Team
1. Angie Z.
2. Miranda D.
3. Sydney G.
4. Oscar S.
Yellow Team
1. Jesus R.
2. Ariana P.
3. Leslie V.
4. Erick M.
Purple Team
1. James L.
2. Lee Ann Q.
3. Mirna A.
4. Thea Q. Orange Team
1. Christina G.
2. Derek A.
3. Yuleni V.
Geometry Period 6 Teams Red Team
1. Freddy A.
2. Anthony S.
3. Hannya O.
4. Ashley L.
Green Team
1. Christina R.
2. Geovanni B.
3. Oscar G.
4. Sabrina L. Blue Team
1. Jose S.
2. Jailene L.
3. Abigail G.
4. Andy H.
Yellow Team
1. Paulina C.
2. Martin R.
3. Melissa R.
4. Jonathan T.
Purple Team
1. Alexis A.
2. Deborah H.
3. Sabrina O.
4. Cristian B. Orange Team
1. Steven P.
2. Wendy G.
3. Leslie H.
Exercise #1
Find the measure of the unknown angle shown below.
Exercise #2
Find the measure of the unknown angle shown below.
Exercise #3
Find the measure of the unknown angle shown below.
Exercise #4
Find the measure of the unknown angle shown below.
Exercise #5
Find the measure of the unknown angle shown below.
Exercise #6
Find the measure of the unknown angle shown below.
Exercise #7
Find the measure of the unknown angle shown below.
Exercise #8
Find the measure of the unknown angle shown below.
Exercise #9
Find the measure of the unknown angle shown below.
Exercise #10
Find the measure of the unknown angle shown below.
Triangle Sum Theorem Masters Period 1
1. Mario L.
2. Evelyn C.
3. Alejandra P.
4. Monica G.
Period 2
1. Miguel B.
2. Jose L.
3. Jackie D.
4. Carina
Period 4
1. Jesus R.
2. Ariana P.
3. Leslie V.
4. Eric M.
Period 5
Period 3
1. Stephanie L.
2. Adrian D.
3. Armando H.
4. Karla L. Period 6
1. Oscar G.
2. Christina R.
3. Sabrina L.
4. Geo B.
Closure
Take a moment to response to the following prompts on a flashcard.
Why do the angles of any triangle add up to 180 degrees?
The angles of any triangle add up to 180 degrees because ___________________________ .
What conditions must three sides satisfy in order for the sides to form a triangle?
In order for sides to form a triangle, _____________________ .
