1. Theorem: If two segments from the same exterior point are tangent to a circle, then the two
segments are congruent.
Given: EM and EL are tangent to OS at M and L respectively.
Prove: EM E EL
s
M
E
Proof:
Reason
Statement
Radii of the same circle are congruent.
MS LS
ELLS and EMMS
ES ES
Hypotenuse-Leg Congruence Theorem
CPCTC
EM EL
segments are congruent.
Given: EM and EL are tangent to OS at M and L respectively.
Prove: EM E EL
s
M
E
Proof:
Reason
Statement
Radii of the same circle are congruent.
MS LS
ELLS and EMMS
ES ES
Hypotenuse-Leg Congruence Theorem
CPCTC
EM EL
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Answers & Comments
Answer:
EL⊥LS and EM⊥MS- tangent line is perpendicular to circle
ES≅ES- Reflexive Property
ΔELS≅ΔEMS- Hypotenuse-Leg Congruence Theorem