Respuesta :

Answer:

See Below.

Step-by-step explanation:

We are given that:

[tex]EL\cong KP[/tex]

And we want to prove that:

[tex]KE\cong LP[/tex]

Congruent chords have congruent arcs. Therefore:

[tex]\stackrel{\frown}{EL}\, \cong \, \stackrel{\frown}{KP}[/tex]

Arc EL is the sum of Arcs LP and PE:

[tex]\stackrel{\frown}{EL}\,=\, \stackrel{\frown}{LP}+\stackrel{\frown}{PE}[/tex]

Likewise, Arc KP is the sum of Arcs KE and PE:

[tex]\stackrel{\frown}{KP}\, =\, \stackrel{\frown}{KE}+\stackrel{\frown}{PE}[/tex]

Since Arcs EL and KP are congruent:

[tex]\stackrel{\frown}{LP}+\stackrel{\frown}{PE}\, =\, \stackrel{\frown}{KE}+\stackrel{\frown}{PE}[/tex]

Subtraction Property of Equality:

[tex]\stackrel{\frown}{LP} \, \cong\, \stackrel{\frown}{KE}[/tex]

Congruent arcs have congruent chords. Therefore:

[tex]LP\cong KE[/tex]

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