Download November 15, 2012 1. DE ≅ HG 1. Given 2. DF ≅ HF

November 15, 2012
How to prove two triangles are congruent
1) Label Congruent corresponding
Angles with "A"s
2) Label Congruent corresponding
sides with "S"s
3) You need 3 pairs of A's and 3 pairs
of S's.
______ ≅ ______
∠____ ≅ ∠____
______ ≅ ______
∠____ ≅ ∠____
______ ≅ ______
∠____ ≅ ∠____
4) If congruent; write the congruence
statement: ∆_______ ≅ ∆_______
Looking for ≅ corresponding angles and sides!!! Must have 3
pairs of ≅ angles and 3 pairs of ≅ sides.
Statements
Reasons
1. DE ≅ HG
2. DF ≅ HF
3. EF ≅ GF
1. Given
2. given
3. Given
4. ∠D ≅ ∠H
4. Given
5. ∠DFE ≅ ∠HFG
5. Vertical Angles Theorem
6. ∠E ≅ G
7. ∆DFE ≅ ∆HFG
6. 3rd angle theorem
7. Definition of ≅ Triangles
November 15, 2012
Your turn Prove the triangles are congruent!
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✓Checkpoint
Independent Practice:
>>>>>>Remember<<<<<<
1) Label Congruent corresponding
Angles with "A"s
2) Label Congruent corresponding
sides with "S"s
3) You need 3 pairs of A's and 3 pairs
of S's.
4) If congruent; write the congruence
statement
November 15, 2012
November 15, 2012
Today you will prove congruent triangles by
using
SSS Congruence Postulate
SAS Congruence Postulate
http://www.youtube.com/watch?
v=kSV5Plfbq48&feature=related
http://www.youtube.com/watch?v=_L8u8io6n2A&feature=related
November 15, 2012
November 15, 2012
APK:
In lesson 4.2 we learned that triangles are
congruent if they have the same size, meaning
* Congruent Corresponding Angles
* Congruent Corresponding Sides (segments)
This is why we had to find three pairs of
congruent angles and three pairs of congruent
sides (segments).
Given: ABD
CDB,
ADB
CBD,
AD BC,
AB
DC
Using Third Angle Theorem we can say
that A
C
Using Reflexive Property we can say
that DC DC
So we have three pairs of congruent
angles and three pairs of congruent
sides.
Therefore the triangle are congruent.
How do we format this prove in a
two column proof?
Easy
Given: ABD
AD BC, AB
Prove: ∆ABD
CDB, ADB
DC
∆CDB
Statements
1. ∠ABD ≅ ∠CDB
2. ∠ADB ≅ ∠CBD
3. ∠A ≅ ∠C
4. AD ≅ BC
5. AB ≅ DC
6. DB ≅ DB
7. ∆ABD ≅ ∆CDB
CBD,
Reasons
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November 15, 2012
Front Loading... White boards!
November 15, 2012
Proving Triangles Are Congruent
Name:_________________________ Period#:______
Practice:
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B
D
C
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PROVE:
November 15, 2012
Homework
November 15, 2012
Today you will prove congruent triangles by
using
AAS Congruence Theorem
ASA Congruence Postulate
November 15, 2012
, ∠ACB ≅ ∠DCE
November 15, 2012
Complete the following proof.
November 15, 2012
November 15, 2012
November 15, 2012
Homework
November 15, 2012
Today you will prove congruent triangles by using
SSS Congruence Postulate
SAS Congruence Postulate
AAS Congruence Theorem
ASA Congruence Postulate
HL Congruence Theorem
November 15, 2012
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4.
Practice All Triangle Congruency Theorems and Postulates:
November 15, 2012
Homework
November 15, 2012