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Write a Paragraph Proof.
Given: Line BC is congruent to line EC and line AC is congruent to line DC
Prove: Line BA Is congruent to Line ED

Write a Paragraph Proof Given Line BC is congruent to line EC and line AC is congruent to line DC Prove Line BA Is congruent to Line ED class=
Write a Paragraph Proof Given Line BC is congruent to line EC and line AC is congruent to line DC Prove Line BA Is congruent to Line ED class=

Respuesta :

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The given states that line BC is congruent to line EC and line AC is congruent to line DC. By the vertical angles theorem, angle BCA is congruent to angle DCE. By SAS, triangle BCA is congruent to triangle DCE. Using CPCTC, it can be concluded that line BA is congruent to line ED.

A paragraph proof with all the statements and reasons to Prove that Line BA Is congruent to Line ED are given below.

We are given that line BC is congruent to line EC and line AC is congruent to line DC. Thus;

Statement 1; BC ≅ EC

Reason 1; Given

Statement 2; AC ≅ DC

Reason 2; Given

Statement 3; ∠BCA ≅ ∠DCE

Reason 3; Vertical angles theorem

Statement 4; ΔBCA ≅ DCE

Reason 4; SAS Congruence Postulate

Statement 5; BA ≅ ED

Reason 5; CPCTC; Corresponding Parts of a Congruent Triangle are Congruent.

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