Q
QuestionMathematics

Using CPCTC ( one posted had partial but I wanted to help ya all who nee this , I figured it out:) Using Triangle Congruence Theorems Given: AD =BC and Prove: DE = CE # Using CPCTC Given: $\overline{A D} \cong \overline{B C}$ and $\angle B C D \cong \angle A D C$ Prove: $\overline{D E} \cong \overline{C E}$ | Angles | Segments | Triangles | Statements | Reasons | | | --- | --- | --- | --- | --- | --- | | $\cong$ | $\angle A D C$ | $\angle B C D$ | $\angle C B E$ | $\angle C E B$ | $\angle D A E$ | | $\angle D E A$ | $\angle E C D$ | $\angle E D C$ | | | | ## Statements $\checkmark$ 2. $\angle B C D \cong \angle A D C$ $\checkmark$ 3. $\overline{D C} \cong \overline{D C}$ $\checkmark$ 4. $\triangle A D C \cong \triangle B C D$ $\checkmark$ 5. $\angle D A E \cong \angle C B E$ $\checkmark$ 6. $\angle D E A$ and $\angle C E B$ are vertical angles $\checkmark$ 7. $\angle D E A \cong \angle C E B$ $\checkmark$ 8. $\triangle A E D \cong \triangle B E C$ $\checkmark$ 9. $\overline{D E} \cong \overline{C E}$ ## Reasons 2. given 3. reflexive property 4. SAS 5. CPCTC 6. def. of vertical angles 7. vertical angles theorem 8. AAS 9. CPCTC Given: AD ≅ BC and ∠BCD ≅ ∠ADC Prove: DE ≅ CE This task is complete.

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Answer

Full Solution Locked

Step 1:
I'll solve this geometry proof using CPCTC (Corresponding Parts of Congruent Triangles are Congruent) with precise LaTeX formatting:

Step 2:
: Identify Given Information

- $$\overline{AD} \cong \overline{BC}

- \angle BCD \cong \angle ADC

Step 3:
: Prove Congruence of \triangle ADC and \triangle BCD

- By SAS (Side-Angle-Side) Congruence Theorem, $$\triangle ADC \cong \triangle BCD

- Side \overline{DC} is common to both triangles (reflexive property)

Step 4:
: Use CPCTC to Establish Angle Congruence

- $$\angle DAE \cong \angle CBE

- Corresponding angles from congruent triangles are congruent

Step 5:
: Identify Vertical Angles

- $$\angle DEA \cong \angle CEB

- Vertical angles are congruent

Step 6:
: Prove Congruence of \triangle AED and \triangle BEC

- By AAS (Angle-Angle-Side) Congruence Theorem, $$\triangle AED \cong \triangle BEC

- \angle DEA \cong \angle CEB (vertical angles)

Final Answer

By CPCTC, \overline{DE} \cong \overline{CE}

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Q
QuestionMathematics

Answer

Full Solution Locked

Step 1:
I'll solve this geometry proof using CPCTC (Corresponding Parts of Congruent Triangles are Congruent) with precise LaTeX formatting:

Step 2:
: Identify Given Information

Step 3:
: Prove Congruence of \triangle ADC and \triangle BCD

Step 4:
: Use CPCTC to Establish Angle Congruence

Step 5:
: Identify Vertical Angles

Step 6:
: Prove Congruence of \triangle AED and \triangle BEC

Final Answer

Need Help with Homework?

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QQuestionMathematics

AnswerHelpful

Full Solution Locked

Step 1:I'll solve this geometry proof using CPCTC (Corresponding Parts of Congruent Triangles are Congruent) with precise LaTeX formatting:

Step 2:: Identify Given Information

Step 3:: Prove Congruence of \triangle ADC and \triangle BCD

Step 4:: Use CPCTC to Establish Angle Congruence

Step 5:: Identify Vertical Angles

Step 6:: Prove Congruence of \triangle AED and \triangle BEC

Final Answer

Need Help with Homework?

Related Questions

Q
QuestionMathematics

Answer

Step 1:
I'll solve this geometry proof using CPCTC (Corresponding Parts of Congruent Triangles are Congruent) with precise LaTeX formatting:

Step 2:
: Identify Given Information

Step 3:
: Prove Congruence of \triangle ADC and \triangle BCD

Step 4:
: Use CPCTC to Establish Angle Congruence

Step 5:
: Identify Vertical Angles

Step 6:
: Prove Congruence of \triangle AED and \triangle BEC