Lesson 4.3

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Transcript Lesson 4.3 

4-3 Triangle
Congruence
by ASA and
AAS
Notes
ο‚›ASA-
Angle, side, angle (must
be in order!!)
ο‚›AAS-
Angle, angle, side (must
be in order!!!)
Theorem!
Example 1
Example 2
1.
2.
3.
4.
Statements
∠𝐢𝐴𝐡 β‰… ∠𝐷𝐴𝐸 π‘Žπ‘›π‘‘ 𝐴𝐡 β‰… 𝐴𝐸
∠ABC and ∠𝐴𝐸𝐷 π‘Žπ‘Ÿπ‘’ π‘Ÿπ‘–π‘”β„Žπ‘‘ π‘Žπ‘›π‘”π‘™π‘’π‘ 
∠𝐴𝐡𝐢 β‰… ∠𝐴𝐸𝐷
βˆ†π΄π΅πΆ β‰… βˆ†π΄πΈπ·
Reasons
1.
2.
3.
4.
𝐺𝑖𝑣𝑒𝑛
G𝑖𝑣𝑒𝑛
π‘…π‘–π‘”β„Žπ‘‘ 𝐴𝑛𝑔𝑙𝑒𝑠 πΆπ‘œπ‘›π‘”π‘Ÿπ‘’π‘’π‘›π‘π‘’ π‘‡β„Žπ‘š
𝐴𝑛𝑔𝑙𝑒 βˆ’ 𝑆𝑖𝑑𝑒 βˆ’ 𝐴𝑛𝑔𝑙𝑒 𝐴𝑆𝐴 π‘‡β„Žπ‘š
Example 3
ο‚› Try
this proof on your own!
Statements
1. 𝑁𝑀 β‰… 𝑁𝑃 π‘Žπ‘›π‘‘ βˆ π‘€ β‰… βˆ π‘ƒ
2. ∠MNL β‰… βˆ π‘ƒπ‘π‘‚
3. βˆ†π‘π‘€πΏ β‰… βˆ†π‘π‘ƒπ‘‚
Reasons
1. 𝐺𝑖𝑣𝑒𝑛
2. π‘‰π‘’π‘Ÿπ‘‘π‘–π‘π‘Žπ‘™ 𝐴𝑛𝑔𝑙𝑒𝑠 π‘‡β„Žπ‘š
3. 𝐴𝑆𝐴
Theorem
Example 4
Practice
ο‚› Pg.
197-198 #1-2, 5-11, 13, 14-18, and 29