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"Tangent Proof"
供稿人: Smith
Prove ∆EMC is ≅ to  ∆ETC
ET  and EM are tangent to ◉ C
Statements will be given for this proof
Choose the appropriate reason.

All reason answer choices are mathematically true.
Pick the one that explains each statement.
E
M
C
T
ET  and EM are
tangent to ◉ C
Statements
? WHY ?
Reasons
E
Given
Taken
M
C
T
ET  and EM are ≅
Statements
ET  and EM are
tangent to ◉ C
Reasons
? WHY ?
Hat Theorem (twin tangents are ≅)
               
Given
 Tangents and radii form right angles
Radii of a circle are ≅
E
M
C
T
ET  and EM are ≅
Statements
EC is ≅ to EC
ET  and EM are
tangent to ◉ C
Reflexive Property (segments are ≅ to themselves)
Hat Theorem (Twin Tangents are ≅)
 All radii from the same circle are ≅
Hat Theorem
Reasons
Given
? WHY ?
E
M
C
T
ET  and EM are ≅
Statements
EC is ≅ to EC
MC is ≅ to TC
ET  and EM are
tangent to ◉ C
Reflexive Property
Hat Theorem
Reasons
Given
? WHY ?
Tangents and radii form right angles
The radius is half the diameter
 All radii from the same circle are ≅
E
M
C
T
∆EMC is ≅ to ∆ETC
ET  and EM are ≅
Statements
EC is ≅ to EC
MC is ≅ to TC
ET  and EM are
tangent to ◉ C
Reflexive Property
Circle radii are ≅
Hat Theorem
Reasons
? WHY ?
Given
 SAS (Side Angle Side)
 SSS  (Side Side Side)
ASA (Angle Side Angle)
E
M
C
T
∆EMC is ≅ to ∆ETC
ET  and EM are ≅
Statements
EC is ≅ to EC
MC is ≅ to TC
ET  and EM are
tangent to ◉ C
Reflexive Property
Circle radii are ≅
Hat Theorem
Reasons
SSS
Given
Click OK
E
M
C
T
"FINAL EXAM"
∆EMC is ≅ to ∆ETC
ET  and EM are ≅
Statements
EC is ≅ to EC
MC is ≅ to TC
ET  and EM are
tangent to ◉ C
Reflexive Property
?
Circle radii are ≅
?
Hat Theorem
?
Reasons
Given
?
SSS
?
E
M
C
T
The End
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