Given: EL≅KP Prove: KE≅LP

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]