Question

a proof of the base angle theorem is shown.

given: $overline{ac} \cong \overline{bc}$ and $overline{cd} \perp \overline{ab}$
prove: the base angles of $\triangle abc$
are congruent.

proof:

statements

reasons

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1. $overline{ac} \cong \overline{bc}$ and $overline{cd} \perp \overline{ab}$

1. given

2. _______________

2. reflexive property

3. _______________

3. definition of perpendicular lines

4. _______________

4. hl theorem

5. _______________

5. cpctc

Explanation:

Step1: Identify reflexive side

$\overline{CD} \cong \overline{CD}$

Step2: Mark right angles

$\angle ADC$ and $\angle BDC$ are right angles ($\angle ADC = \angle BDC = 90^\circ$)

Step3: Prove triangle congruence

$\triangle ADC \cong \triangle BDC$

Step4: State congruent base angles

$\angle A \cong \angle B$

Answer:

Statements	Reasons
2. $\overline{CD} \cong \overline{CD}$	2. Reflexive property
3. $\angle ADC = \angle BDC = 90^\circ$	3. Definition of perpendicular lines
4. $\triangle ADC \cong \triangle BDC$	4. HL theorem
5. $\angle A \cong \angle B$	5. CPCTC

Final proven result: The base angles of $\triangle ABC$ ($\angle A$ and $\angle B$) are congruent.