Name: ____________________________________________ Date: ______ Ms. Ayinde Geometry CC Objective: To prove two triangles congruent using SSS, SAS, ASA, AAS, or HL. To prove a pair of corresponding parts (angles or sides) are congruent in congruent triangles. For this project, you will be working in groups to complete the following:

1. Take neat and organized notes on how and why we use the “I Know, I Plan, and I Prove” method when proof writing.

2. After taking notes, complete the accompanying proof packet in pencil with your group. 3. Each scholar will be given a specific concept (SSS, SAS, ASA, AAS, HL, CPCTC). You

must create an original proof using the concept assigned. Each proof must include: a. A blank version of the problem with a diagram, given information, and a prove

statement. b. Two answer keys for the proof.

You will be given from 1/7/19 to 1/10/19 to complete the notes, to complete the packet, and to create your own proof question. Work must be submitted daily. All required classwork will be collected and checked at the end of class. All homework will be collected and checked at the beginning of each class. The required classwork and homework for each day is listed below. Time Line Classwork Homework Day 1 1. Take notes on SSS, SAS,

ASA, AAS, and HL.

1. Take notes on CPCTC. 2. Complete proof questions

#1-4.

Day 2 1. Complete proof questions #5-8.

1. Complete proof questions #9-12

Day 3 1. Complete proof

questions #13-14. 2. Create an original

proof question using your assigned method.

1. Complete definitions, properties, postulates, and theorems reference sheet.

Day 4 1. Create two answer keys for your proof question.

1. Study for quiz.

You will receive two grades for this project:

1. Classwork Grade 2. Homework Grade

The accompanying rubric will be used to assess your work throughout this project. You will take a quiz following this project to assess your knowledge on proof writing.

Student Name: _______________________________________________________ Date: _____________

Rubric 4: Excellent 3: On Track 2: Below Expectations 1: Needs Improvement 0: Unsatisfactory Daily

Score Day 1

Classwork and

Teamwork

Neat and organized notes. Includes how and when to use SSS, SAS, ASA, AAS, and HL. Includes why and how to use “I Know, I Plan, I Prove”.

Somewhat neat and organized notes. Mostly includes how and when to use SSS, SAS, ASA, AAS, and HL. Includes why and how to use “I Know, I Plan, I Prove”.

Sloppy notes. Mostly includes how and when to use SSS, SAS, ASA, AAS, and HL. Includes why and how to use “I Know, I Plan, I Prove”.

Sloppy notes. Little to no notes including how and when to use SSS, SAS, ASA, AAS, HL, and “I Know, I Plan, I Prove”.

No work is submitted or none of the work is accurate.

____/8 Always on task and split the work evenly. Worked well together.

Mostly on task and the work is split evenly. Worked well together.

Lost focus, and the work is not split evenly. Had some difficulties working together.

Barely on task and did not split up the work evenly. Did not work well together.

Group members work separately.

Day 1 Homework

Neat and organized notes. Includes how and when to use CPCTC. The problem set and reference sheet are completed accurately with little to no mistakes and includes all appropriate work.

Somewhat neat and organized notes. Mostly includes how and when to use CPCTC. The problem set and reference sheet are mostly accurate with a few mistakes and includes most of the appropriate work.

Sloppy notes. Mostly includes how and when to use CPCTC. The problem set and reference sheet are somewhat accurate with a few mistakes and includes some appropriate work.

Sloppy notes. Little to no notes including how and when to use CPCTC. The problem set and reference sheet are incomplete, missing a lot of work, or has numerous mistakes.

No work is submitted or none of the work is accurate.

____/4

Day 2 Classwork

and Teamwork

The problem set is completed accurately with little to no mistakes and includes all appropriate work.

The problem set is mostly accurate with a few mistakes and includes most of the appropriate work.

The problem set is somewhat accurate with a few mistakes and includes some appropriate work.

The problem set is incomplete, missing a lot of work, or has numerous mistakes.

No work is submitted or none of the work is accurate.

____/8 Always on task and split the work evenly. Worked well together.

Mostly on task and the work is split evenly. Worked well together.

Lost focus, and the work is not split evenly. Had some difficulties working together.

Barely on task and did not split up the work evenly. Did not work well together.

Group members work separately.

Day 2 Homework

The problem set is completed accurately with little to no mistakes and includes all appropriate work.

The problem set is mostly accurate with a few mistakes and includes most of the appropriate work.

The problem set is somewhat accurate with a few mistakes and includes some appropriate work.

The problem set is incomplete, missing a lot of work, or has numerous mistakes.

No work is submitted or none of the work is accurate.

____/4

Day 3

Classwork and

Teamwork

The problem set is completed accurately with little to no mistakes and includes all appropriate work. The proof is neat and organized. The proof is original and includes given information, a prove statement, a diagram and a blank statement and reasons t-chart.

The problem set is mostly accurate with a few mistakes and includes most of the appropriate work. The proof is somewhat neat and organized. The proof is original and includes given information, a prove statement, a diagram and a blank statement and reasons t-chart.

The problem set is somewhat accurate with a few mistakes and includes some appropriate work. The proof is sloppy and a little unorganized. The proof is original and includes given information, a prove statement, a diagram and a blank statement and reasons t-chart. The proof has a few mistakes or is missing information.

The problem set is incomplete, missing a lot of work, or has numerous mistakes. The proof is sloppy and very unorganized. The proof is original and includes given information, a prove statement, a diagram and a blank statement and reasons t-chart. The proof has several mistakes or is missing information.

No work is submitted or none of the work is accurate.

____/8

Always on task and split the work evenly. Worked well together.

Mostly on task and the work is split evenly. Worked well together.

Lost focus, and the work is not split evenly. Had some difficulties working together.

Barely on task and did not split up the work evenly. Did not work well together.

Group members work separately.

Day 4 Classwork and Teamwork

There are two neatly written answer keys. The answer keys are accurate.

There are two somewhat neat answer keys. The answer keys are mostly accurate with a few mistakes.

There are two sloppy answer keys. The answer keys are somewhat accurate with a few mistakes

There is one neatly written answer key.

No work is submitted or none of the work is accurate.

____/8 Always on task and split the work evenly. Worked well together.

Mostly on task and the work is split evenly. Worked well together.

Lost focus, and the work is not split evenly. Had some difficulties working together.

Barely on task and did not split up the work evenly. Did not work well together.

Group members work separately.

Final Classwork Grade: _____/32 Final Homework Grade: ______/8 Comments: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________

Reference Sheet

Reference Sheet

Name: ________________________________________________Date: ___________________ Ms. Ayinde Proving Triangles Congruent Write a proof for each of the following. Fill in the I Know, I Plan, I Prove boxes #1-8. For #9-14, use of I Know, I Plan, I Prove is optional.

1.

I KNOW:

I PROVE

I PLAN: SSS SAS ASA AAS HL

2.

I KNOW:

I PROVE

I PLAN: SSS SAS ASA AAS HL

3.

I KNOW:

I PROVE

I PLAN: SSS SAS ASA AAS HL

4.

I KNOW:

I PROVE

I PLAN: SSS SAS ASA AAS HL

5.

I KNOW:

I PROVE

I PLAN: SSS SAS ASA AAS HL

6.

I KNOW:

I PROVE

I PLAN: SSS SAS ASA AAS HL

7.

I KNOW:

I PROVE

I PLAN: SSS SAS ASA AAS HL

8.

I KNOW:

I PROVE

I PLAN: SSS SAS ASA AAS HL

9.

10.

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Geometry,)Unit)5)–)Congruent)Triangles)Proof)Activity)–)Part)I) Name%_________________________%)For%each%problem,%do%the%following:%

a. Show%the%given%information%in%the%diagram%(using%tick%marks%to%show%congruent%sides%and%arcs%to%show%congruent%angles)%

b. Show%any%other%congruent%parts%you%notice%(from%vertical%angles,%sides%shared%in%common,%or%alternate%interior%angles%with%parallel%lines)%

c. Give%the%postulate%or%theorem%that%proves%the%triangles%congruent%(SSS,%SAS,%ASA,%AAS,%HL)%d. Finally,%fill%in%the%blanks%to%complete%the%proof.%

%1.%%% % % Given:%%BC ≅ DC ;%AC ≅ EC %%%%%%% % % Prove:%%ΔBCA ≅ ΔDCE %%

Statements% Reasons%

1.% 1.%%Given%

2.% 2.%%Vertical%∠s%Theorem%

3.%ΔBCA ≅ ΔDCE % 3.%

%%2.%%%%%% % % Given:%% JK ≅ LK ;% JM ≅ LM %% % % Prove:%%ΔKJM ≅ ΔKLM %%

Statements% Reasons%

1.% 1.%

2.% 2.%%Reflexive%Prop.%

3.% 3.%

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Statements% Reasons%

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3.%%% 3.%%Reflexive%Prop.%

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a. Show%the%given%information%in%the%diagram%(using%tick%marks%to%show%congruent%sides%and%arcs%to%show%congruent%angles)%

b. Show%any%other%congruent%parts%you%notice%(from%vertical%angles,%sides%shared%in%common,%or%alternate%interior%angles%with%parallel%lines)%

c. Give%the%postulate%or%theorem%that%proves%the%triangles%congruent%(SSS,%SAS,%ASA,%AAS,%HL)%d. Finally,%fill%in%the%blanks%to%complete%the%proof.%

%1.%%% % % Given:%%BC ≅ DC ;%AC ≅ EC %%%%%%% % % Prove:%%ΔBCA ≅ ΔDCE %%

Statements% Reasons%

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2.% 2.%%Vertical%∠s%Theorem%

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Statements% Reasons%

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3.%%% 3.%%Reflexive%Prop.%

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11.

12.

13.

C

B

A

D

E

F H

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Geometry,)Unit)5)–)Congruent)Triangles)Proof)Activity)–)Part)I) Name%_________________________%)For%each%problem,%do%the%following:%

a. Show%the%given%information%in%the%diagram%(using%tick%marks%to%show%congruent%sides%and%arcs%to%show%congruent%angles)%

b. Show%any%other%congruent%parts%you%notice%(from%vertical%angles,%sides%shared%in%common,%or%alternate%interior%angles%with%parallel%lines)%

c. Give%the%postulate%or%theorem%that%proves%the%triangles%congruent%(SSS,%SAS,%ASA,%AAS,%HL)%d. Finally,%fill%in%the%blanks%to%complete%the%proof.%

%1.%%% % % Given:%%BC ≅ DC ;%AC ≅ EC %%%%%%% % % Prove:%%ΔBCA ≅ ΔDCE %%

Statements% Reasons%

1.% 1.%%Given%

2.% 2.%%Vertical%∠s%Theorem%

3.%ΔBCA ≅ ΔDCE % 3.%

%%2.%%%%%% % % Given:%% JK ≅ LK ;% JM ≅ LM %% % % Prove:%%ΔKJM ≅ ΔKLM %%

Statements% Reasons%

1.% 1.%

2.% 2.%%Reflexive%Prop.%

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3.%%% 3.%%Reflexive%Prop.%

4.% 4.%

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C

B

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D

E

F H

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a. Show%the%given%information%in%the%diagram%(using%tick%marks%to%show%congruent%sides%and%arcs%to%show%congruent%angles)%

b. Show%any%other%congruent%parts%you%notice%(from%vertical%angles,%sides%shared%in%common,%or%alternate%interior%angles%with%parallel%lines)%

c. Give%the%postulate%or%theorem%that%proves%the%triangles%congruent%(SSS,%SAS,%ASA,%AAS,%HL)%d. Finally,%fill%in%the%blanks%to%complete%the%proof.%

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Statements% Reasons%

1.% 1.%%Given%

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Statements% Reasons%

1.% 1.%

2.% 2.%%Reflexive%Prop.%

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3.%%% 3.%%Reflexive%Prop.%

4.% 4.%

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14.

C

B

A

D

E

F H

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Geometry,)Unit)5)–)Congruent)Triangles)Proof)Activity)–)Part)I) Name%_________________________%)For%each%problem,%do%the%following:%

a. Show%the%given%information%in%the%diagram%(using%tick%marks%to%show%congruent%sides%and%arcs%to%show%congruent%angles)%

b. Show%any%other%congruent%parts%you%notice%(from%vertical%angles,%sides%shared%in%common,%or%alternate%interior%angles%with%parallel%lines)%

c. Give%the%postulate%or%theorem%that%proves%the%triangles%congruent%(SSS,%SAS,%ASA,%AAS,%HL)%d. Finally,%fill%in%the%blanks%to%complete%the%proof.%

%1.%%% % % Given:%%BC ≅ DC ;%AC ≅ EC %%%%%%% % % Prove:%%ΔBCA ≅ ΔDCE %%

Statements% Reasons%

1.% 1.%%Given%

2.% 2.%%Vertical%∠s%Theorem%

3.%ΔBCA ≅ ΔDCE % 3.%

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a. Show%the%given%information%in%the%diagram%(using%tick%marks%to%show%congruent%sides%and%arcs%to%show%congruent%angles)%

b. Show%any%other%congruent%parts%you%notice%(from%vertical%angles,%sides%shared%in%common,%or%alternate%interior%angles%with%parallel%lines)%

c. Give%the%postulate%or%theorem%that%proves%the%triangles%congruent%(SSS,%SAS,%ASA,%AAS,%HL)%d. Finally,%fill%in%the%blanks%to%complete%the%proof.%

%1.%%% % % Given:%%BC ≅ DC ;%AC ≅ EC %%%%%%% % % Prove:%%ΔBCA ≅ ΔDCE %%

Statements% Reasons%

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