complete the proof.

given: isoceles triangle $\delta abc$

prove: $\angle bac \cong \angle bca$

statements | reasons
--- | ---
1) isoceles triangle $\delta abc$ | given
2) $d$ is midpoint of $\overline{ac}$ | dropdown
3) $\overline{ad} \cong \overline{cd}$ | definition of midpoint
4) $bd = db$ | transitive property
5) $\delta abd \cong \delta cbd$ | dropdown
6) $\angle bac \cong \angle bca$ | dropdown

Question

complete the proof.

given: isoceles triangle $\delta abc$

prove: $\angle bac \cong \angle bca$

statements | reasons
--- | ---
1) isoceles triangle $\delta abc$ | given
2) $d$ is midpoint of $\overline{ac}$ | dropdown
3) $\overline{ad} \cong \overline{cd}$ | definition of midpoint
4) $bd = db$ | transitive property
5) $\delta abd \cong \delta cbd$ | dropdown
6) $\angle bac \cong \angle bca$ | dropdown

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Geometric Proofs", "Isosceles Triangle Theorem" ], "current_concepts": [ "Geometric Proofs", "Isosceles Triangle Theorem", "Triangle Congruence" ] } ## Identificar la justificación para el paso 2 $$ \text{Paso 2: } D \text{ is midpoint of } \overline{AC} \implies \text{By construction of midpoint } D $$ ## Identificar la justificación para el paso 5 $$ \text{Paso 5: } \triangle ABD \cong \triangle CBD \implies \text{SSS Congruence Postulate} $$ ## Identificar la justificación para el paso 6 $$ \text{Paso 6: } \angle BAC \cong \angle BCA \implies \text{CPCTC} $$ Complete the proof. Given: Isoceles triangle $\triangle ABC$ Prove: $\angle BAC \cong \angle BCA$ | Statements | Reasons | | :--- | :--- | | 1) Isoceles triangle $\triangle ABC$ | Given | | 2) $D$ is midpoint of $\overline{AC}$ | By construction of midpoint D | | 3) $\overline{AD} \cong \overline{CD}$ | Definition of midpoint | | 4) $\overline{BD} \cong \overline{DB}$ | Reflexive Property | | 5) $\triangle ABD \cong \triangle CBD$ | SSS | | 6) $\angle BAC \cong \angle BCA$ | CPCTC | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Geometric Proofs" ] }

Statements	Reasons
2) \(D\) is midpoint of \(\overline{AC}\)	<blank>By construction of midpoint D</blank>
3) \(\overline{AD} \cong \overline{CD}\)	Definition of midpoint
4) \(\overline{BD} \cong \overline{DB}\)	Reflexive Property
5) \(\triangle ABD \cong \triangle CBD\)	<blank>SSS</blank>
6) \(\angle BAC \cong \angle BCA\)	<blank>CPCTC</blank>

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QUESTION IMAGE

Question

Explanation:

Identificar la justificación para el paso 2

Identificar la justificación para el paso 5

Identificar la justificación para el paso 6

Answer: