contestada

Zoe tried to prove that △ A E D ≅ △ C E B △AED≅△CEBtriangle, A, E, D, \cong, triangle, C, E, B. D D A A E E B B C C Statement Reason 1 ∠ A ≅ ∠ C ∠A≅∠Cangle, A, \cong, angle, C Given 2 ∠ D E A ≅ ∠ B E C ∠DEA≅∠BECangle, D, E, A, \cong, angle, B, E, C Given 3 A E ‾ ≅ E C ‾ AE ≅ EC start overline, A, E, end overline, \cong, start overline, E, C, end overline Given 4 △ A E D ≅ △ C E B △AED≅△CEBtriangle, A, E, D, \cong, triangle, C, E, B Angle-side-angle congruence

Respuesta :

The reason given for the statement are based on information from

the question, or a postulate or theorem.

  • The first error Zoe made is the error in the reason for statement 2.   ∠DEA ≅ ∠BEC        [tex]{}[/tex]    Given

Reasons:

The two column proof in the question is presented as follows;

Statement             [tex]{}[/tex]          Reason

1. ∠A ≅ ∠C            [tex]{}[/tex]          Given

2. ∠DEA ≅ ∠BEC        [tex]{}[/tex]    Given (Error)

3. [tex]\overline{AE}[/tex] ≅ [tex]\overline{EC}[/tex]            [tex]{}[/tex]         Given

4. ΔAED ≅ ΔCEB         [tex]{}[/tex]   Angle-Side-Angle congruence

Required:

The first error made in the proof

Solution:

The first error made in the above proof is the reason for statement 2.

2. ∠DEA ≅ ∠BEC [tex]{}[/tex]   Given (Error)

The correct reason is as follows;

2. ∠DEA ≅ ∠BEC [tex]{}[/tex]   Vertical angle postulate

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Answer:

A. Zoe used an invalid reason to justify the congruence of a pair of sides or angles.

Step-by-step explanation:

Step 1

The diagram does support the claim that \angle A \cong \angle C∠A≅∠Cangle, A, \cong, angle, C because they both have double arcs.

Step 1 is correct.

Step 2

The diagram does not give us congruence symbols or equal measures for \angle DEA∠DEAangle, D, E, A and \angle BEC∠BECangle, B, E, C.

Zoe needed to justify this step by stating that vertical angles are congruent.

Zoe used an invalid reason to justify the congruence of a pair of sides or angles.

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