Geometry4.3CongruentTriangles

Mr.Deyo

Bytheendoftheperiod,studentswillusepropertiesofcongruenttrianglesandprovetrianglescongruentbyusingthedefinitionofcongruence.

Studentswilldemonstratethisbycompletingagraphicorganizerandbysolvingproblemsinapairactivity.

Learning Target

HomeWork1‐2‐3:1)StormCheckPastedinNotebook?

2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?

Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1.  How are the two pictures similar? 2.  How are they different? 3.  How can these two pictures be related to math?

1)  Congruent

2)  Side

3) Angle

4) Hypotenuse

5)  Leg

Vocabulary

DAY 3 and/or DAY 4 1. Review the word

♦ Friendly Definition ♦ Physical Representation

2. Show how the word works ♦ Synonyms/antonym ♦ Word Problems ♦ Related words/phrases ♦ Example/non-example

Friendly Definition Sketch

Wordwork Sentence

DAY 2 1. Review word

♦ Friendly Definition ♦ Physical Representation

2. Draw a sketch

DAY 5 1. Review the word

♦ Friendly definition ♦ Physical Representation

3. Write a sentence  at least 2 rich words (1 action)  correct spelling  correct punctuation  correct subject/predicate agreement  clear and clean writing

DAY 1 1.  Use Visuals

2.  Introduce the word ♦ Friendly Definition ♦ Physical Representation

3.  Use Cognates

4.  Write friendly definition

5.  Physical Representation

WordList1.  2.  3.  4. 

Notes:

WhenyouwriteastatementsuchasΔABC≅ΔDEF,youarealsostatingwhichpartsarecongruent.

A‐BProblemAnotes:Given: PR and QT bisect each other. ∠PQS ≅ ∠RTS, QP ≅ RT

Prove: ∆QPS ≅ ∆TRS

A‐BProblemACheck:

7. Def. of ≅ ∆s 7. ∆QPS ≅ ∆TRS 6. Third ∠s Thm. 6. ∠QSP ≅ ∠TRS 5. Vert. ∠s Thm. 5. ∠QSP ≅ ∠TSR 4. Def. of bisector 3. Given 2. Given 2. ∠PQS ≅ ∠RTS 1. Given 1. QP ≅ RT

3. PR and QT bisect each other. 4. QS ≅ TS, PS ≅ RS

A‐BProblemBSOLVE!!

Given: AD bisects BE. BE bisects AD. AB ≅ DE, ∠A ≅ ∠D Prove: ∆ABC ≅ ∆DEC

A‐BProblemBCheck!!

6. Def. of bisector

7. Def. of ≅ ∆s 7. ∆ABC ≅ ∆DEC

5. Given

3. ∠ABC ≅ ∠DEC

4. Given

2. ∠BCA ≅ ∠DCE

3. Third ∠s Thm.

2. Vertical ∠s are ≅.

1. Given 1. ∠A ≅ ∠D

4. AB ≅ DE

BE bisects AD

5. AD bisects BE,

6. BC ≅ EC, AC ≅ DC

StormCheck(Think,Write,Discuss,Report)

Inyourownlife,givetwoexampleswhenwouldyouneedtoknowthattwoobjectsare

exactlythesamesizeandshape.

Inmyownlife,Iwouldneedtoknowthattwo

objectsareexactlythesamesizeandshape

when_________________________________

_______________________________________

andwhen______________________________.

Use the diagram to prove the following.

Prove: ∆JKN ≅ ∆LMN

Given: MK bisects JL. JL bisects MK. JK ≅ ML. JK || ML.

8. ∆JKN≅ ∆LMN 7. ∠KJN ≅ ∠MLN 6. ∠KNJ ≅ ∠MNL

3. ∠JKN ≅ ∠NML

1. JK ≅ ML

4. JL and MK bisect each other.

5. JN ≅ LN, MN ≅ KN

2. JK || ML

A‐BProblemAnotes:

A‐BProblemACheck:

8. Def. of ≅ ∆s 8. ∆JKN≅ ∆LMN 7. Third ∠s Thm. 7. ∠KJN ≅ ∠MLN 6. Vert. ∠s Thm. 6. ∠KNJ ≅ ∠MNL 5. Def. of bisector

4. Given

3. Alt int. ∠s are ≅. 3. ∠JKN ≅ ∠NML

1. Given 1. JK ≅ ML

4. JL and MK bisect each other.

5. JN ≅ LN, MN ≅ KN

2. Given 2. JK || ML

Use the diagram to prove the following.

Prove: ∆JKN ≅ ∆LMN Given: MK bisects JL. JL bisects MK. JK ≅ ML. JK || ML.

A‐BProblemBSOLVE!!

Given: C is the midpoint of BD and AE.

∠A ≅ ∠E, AB ≅ ED

Prove: ∆ABC ≅ ∆EDC

7. 7. ΔABC ≅ ΔEDC

6. 6. ∠B ≅ ∠D

5. 5. ∠ACB ≅ ∠ECD

4. 4. AB ≅ ED

3. 3. AC ≅ EC; BC ≅ DC

2. 2. C is mdpt. of BD and AE

1. 1. ∠A ≅ ∠E

Reasons Statements

A‐BProblemBCheck!!

Given: C is the midpoint of BD and AE.

∠A ≅ ∠E, AB ≅ ED

Prove: ∆ABC ≅ ∆EDC

7. Def. of ≅ ∆s 7. ΔABC ≅ ΔEDC

6. Third ∠s Thm. 6. ∠B ≅ ∠D

5. Vert. ∠s Thm. 5. ∠ACB ≅ ∠ECD

4. Given 4. AB ≅ ED

3. Def. of mdpt. 3. AC ≅ EC; BC ≅ DC

2. Given 2. C is mdpt. of BD and AE

1. Given 1. ∠A ≅ ∠E

Reasons Statements

StormCheck(Think,Write,Discuss,Report)

WheninyourlifedoyouhavetojustifyEVERYTHINGthatyoudo?Givetwoexamples.

Inmyownlife,IhavetojustifyeverythingthatI

dowhen_______________________________

_______________________________________

andwhen______________________________.

HomeWork1‐2‐3:1)StormCheckPastedinNotebook?

2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?

1)  Congruent

2)  Side

3) Angle

4) Hypotenuse

5)  Leg

Vocabulary

Bytheendoftheperiod,studentswillusepropertiesofcongruenttrianglesandprovetrianglescongruentbyusingthedefinitionofcongruence.

Studentswilldemonstratethisbycompletingagraphicorganizerandbysolvingproblemsinapairactivity.

Learning Target

Ticket OUT.

Given: ∆ABC ≅ ∆DEF

Give the reasons in the proof for finding the value of x.

2x – 2 = 6

2x = 8

x = 4

AB ≅ DE

AB = DE

Ticket OUT.

Given: ∆ABC ≅ ∆DEF

Give the reasons in the proof for finding the value of x.

2x – 2 = 6

2x = 8

x = 4

Corr. sides of ≅ ∆s are ≅.

Addition Prop. Of Equality

Division Prop. Of Equality

AB ≅ DE

Substitution of values for AB and DE.

AB = DE Def. of ≅ parts.