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What is the first error Zoe made in her proof?

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

b. Zoe only established some of the necessary conditions for a congruence criterion.

c. Zoe established all necessary conditions, but then used an inappropriate congruence criterion.

d. Zoe used a criterion that does not guarantee congruence

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What is the first error Zoe made in her proofa Zoe used an invalid reason to justify the congruence of a pair of sides or anglesb Zoe only established some of t class=

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Answer:

a

Step-by-step explanation:

To prove congruence

1 ∠ A ≅ ∠ C → given

2 ∠ DEA ≅ ∠ BEC → vertically opposite angles

3. AE ≅ EC → given

We then have 2 angles and the included side ( side between the 2 angles )

congruent in both triangles, thus Δ AED ≅ Δ CEB ( ASA postulate )

Zoes' error was in assuming ∠ DEA ≅ ∠ BEC was given

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

Option a is correct.

From given diagram it is observed that,

Line segment AD and CB are parallel and AC is transversal line. So that alternate angles A and C are equal.

                            [tex]\angle A=\angle C[/tex]

When two lines intersect at any point then vertically opposite angles are equal.

So that,          [tex]\angle DEA=\angle BEC[/tex]

Given that ,   [tex]AE=EC[/tex]

The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Hence, both triangles are congruent to each other.

Learn more:

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