Question

Given: EL≅KP Prove: KE≅LP

Answer 1

Answer:

See Below.

Step-by-step explanation:

We are given that:

$EL\cong KP$

And we want to prove that:

$KE\cong LP$

Congruent chords have congruent arcs. Therefore:

$\stackrel{\frown}{EL}\, \cong \, \stackrel{\frown}{KP}$

Arc EL is the sum of Arcs LP and PE:

$\stackrel{\frown}{EL}\,=\, \stackrel{\frown}{LP}+\stackrel{\frown}{PE}$

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

$\stackrel{\frown}{KP}\, =\, \stackrel{\frown}{KE}+\stackrel{\frown}{PE}$

Since Arcs EL and KP are congruent:

$\stackrel{\frown}{LP}+\stackrel{\frown}{PE}\, =\, \stackrel{\frown}{KE}+\stackrel{\frown}{PE}$

Subtraction Property of Equality:

$\stackrel{\frown}{LP} \, \cong\, \stackrel{\frown}{KE}$

Congruent arcs have congruent chords. Therefore:

$LP\cong KE$