Math / Geometry

QuestionFill in the missing statement and reason of the proof below. Given: $\triangle A B E \cong \triangle C D E$ . Prove: $\overline{B C} \| \overline{A D}$ .
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Statement $A B E \cong \triangle C D E$ $\overline{B E} \cong \overline{D E}$ $\overline{A E} \cong \overline{C E}$ $\triangle B C E \cong \triangle D A E$ Type of Statement $\overline{B C} \| \overline{A D}$
Reason
Given Corresponding Parts of Congruent Triangle are Congruent (CPCTC)
Corresponding Parts of Congruent Triangle are Congruent (CPCTC)
Vertical angles are congruent
SAS
If two lines cut by a transversal form congruent alternate interior angles, then th two lines are parallel /www.deltamath.com/app/student/...

Studdy Solution

STEP 1

1. We are given that $\triangle ABE \cong \triangle CDE$ .
2. We need to prove that $\overline{BC} \parallel \overline{AD}$ .

STEP 2

1. Use the given congruence to establish congruent parts.
2. Identify congruent segments using CPCTC (Corresponding Parts of Congruent Triangles are Congruent).
3. Use properties of angles to establish congruence.
4. Apply the SAS (Side-Angle-Side) congruence postulate.
5. Use the property of parallel lines and alternate interior angles to conclude the proof.

STEP 3

Given: $\triangle ABE \cong \triangle CDE$ .

STEP 4

Statement: $\overline{BE} \cong \overline{DE}$
Reason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

STEP 5

Statement: $\overline{AE} \cong \overline{CE}$
Reason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

STEP 6

Statement: Vertical angles are congruent.
Reason: Vertical angles are congruent.

STEP 7

Statement: $\triangle BCE \cong \triangle DAE$
Reason: SAS (Side-Angle-Side).

STEP 8

Statement: $\overline{BC} \parallel \overline{AD}$
Reason: If two lines cut by a transversal form congruent alternate interior angles, then the two lines are parallel.
The missing statement and reason have been filled in, and the proof is complete.

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Studdy Solution

STEP 1

1. We are given that $\triangle ABE \cong \triangle CDE$ .
2. We need to prove that $\overline{BC} \parallel \overline{AD}$ .

STEP 2

STEP 3

Given: $\triangle ABE \cong \triangle CDE$ .

STEP 4

Statement: $\overline{BE} \cong \overline{DE}$
Reason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

STEP 5

Statement: $\overline{AE} \cong \overline{CE}$
Reason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

STEP 6

Statement: Vertical angles are congruent.
Reason: Vertical angles are congruent.

STEP 7

Statement: $\triangle BCE \cong \triangle DAE$
Reason: SAS (Side-Angle-Side).

STEP 8

Statement: $\overline{BC} \parallel \overline{AD}$
Reason: If two lines cut by a transversal form congruent alternate interior angles, then the two lines are parallel.
The missing statement and reason have been filled in, and the proof is complete.

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Studdy Solution

STEP 1

1. We are given that △ABE≅△CDE\triangle ABE \cong \triangle CDE△ABE≅△CDE.2. We need to prove that BC‾∥AD‾\overline{BC} \parallel \overline{AD}BC∥AD.

STEP 2

STEP 3

Given: △ABE≅△CDE\triangle ABE \cong \triangle CDE△ABE≅△CDE.

STEP 4

Statement: BE‾≅DE‾\overline{BE} \cong \overline{DE}BE≅DEReason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

STEP 5

Statement: AE‾≅CE‾\overline{AE} \cong \overline{CE}AE≅CEReason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

STEP 6

Statement: Vertical angles are congruent.Reason: Vertical angles are congruent.

STEP 7

Statement: △BCE≅△DAE\triangle BCE \cong \triangle DAE△BCE≅△DAEReason: SAS (Side-Angle-Side).

STEP 8

Statement: BC‾∥AD‾\overline{BC} \parallel \overline{AD}BC∥ADReason: If two lines cut by a transversal form congruent alternate interior angles, then the two lines are parallel. The missing statement and reason have been filled in, and the proof is complete.

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1. We are given that $\triangle ABE \cong \triangle CDE$ .
2. We need to prove that $\overline{BC} \parallel \overline{AD}$ .

Given: $\triangle ABE \cong \triangle CDE$ .

Statement: $\overline{BE} \cong \overline{DE}$
Reason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

Statement: $\overline{AE} \cong \overline{CE}$
Reason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

Statement: Vertical angles are congruent.
Reason: Vertical angles are congruent.

Statement: $\triangle BCE \cong \triangle DAE$
Reason: SAS (Side-Angle-Side).

Statement: $\overline{BC} \parallel \overline{AD}$
Reason: If two lines cut by a transversal form congruent alternate interior angles, then the two lines are parallel.
The missing statement and reason have been filled in, and the proof is complete.