complete the two-column proof.

statements | reasons
1) $\delta ghi$, $\overline{of} \parallel \overline{gi}$ | given
2) $\angle igh \cong \angle foh$ and $\angle gih \cong \angle ofh$ | dropdown menu
3) $\delta ghi \sim \delta ohf$ | dropdown menu
4) $\frac{gh}{oh} = \frac{ih}{fh}$ | dropdown menu
5) $gh = go + oh$, $hi = if + fh$ | dropdown menu
6) $\frac{(go + oh)}{oh} = \frac{(if + fh)}{fh}$ | dropdown menu
7) $\frac{go}{oh} + \frac{oh}{oh} = \frac{if}{fh} + \frac{fh}{fh}$ | separation of fractions
8) $\frac{go}{oh} + 1 = \frac{if}{fh} + 1$ | simplify
9) $\frac{go}{oh} = \frac{if}{fh}$ | dropdown menu

dropdown options visible:
corresponding sides of similar triangles are proportional
substitution property of equality
segment addition postulate
corresponding angles theorem
aa similarity theorem
subtraction property of equality

Question

complete the two-column proof.

statements | reasons
1) $\delta ghi$, $\overline{of} \parallel \overline{gi}$ | given
2) $\angle igh \cong \angle foh$ and $\angle gih \cong \angle ofh$ | dropdown menu
3) $\delta ghi \sim \delta ohf$ | dropdown menu
4) $\frac{gh}{oh} = \frac{ih}{fh}$ | dropdown menu
5) $gh = go + oh$, $hi = if + fh$ | dropdown menu
6) $\frac{(go + oh)}{oh} = \frac{(if + fh)}{fh}$ | dropdown menu
7) $\frac{go}{oh} + \frac{oh}{oh} = \frac{if}{fh} + \frac{fh}{fh}$ | separation of fractions
8) $\frac{go}{oh} + 1 = \frac{if}{fh} + 1$ | simplify
9) $\frac{go}{oh} = \frac{if}{fh}$ | dropdown menu

dropdown options visible:
corresponding sides of similar triangles are proportional
substitution property of equality
segment addition postulate
corresponding angles theorem
aa similarity theorem
subtraction property of equality

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Proofs", "Substitution Property" ], "new_concepts": [ "Corresponding Angles Theorem", "Subtraction Property of Equality" ], "current_concepts": [ "Geometric Proofs", "Substitution Property", "Corresponding Angles Theorem", "Subtraction Property of Equality" ] } ## Identificar la razón para el paso 2 $$ \begin{aligned} &\overline{OF} \parallel \overline{GI} \implies \angle IGH \cong \angle FOH \text{ y } \angle GIH \cong \angle OFH \ &\text{Razón: Corresponding Angles Theorem} \end{aligned} $$ ## Identificar la razón para el paso 6 $$ \begin{aligned} &\frac{GH}{OH} = \frac{IH}{FH}, \quad GH = GO + OH, \quad HI = IF + FH \ &\implies \frac{GO + OH}{OH} = \frac{IF + FH}{FH} \ &\text{Razón: Substitution Property of Equality} \end{aligned} $$ ## Identificar la razón para el paso 9 $$ \begin{aligned} &\frac{GO}{OH} + 1 = \frac{IF}{FH} + 1 \implies \frac{GO}{OH} = \frac{IF}{FH} \ &\text{Razón: Subtraction Property of Equality} \end{aligned} $$ ## Question 1 Para el paso 2, la razón correspondiente es Corresponding Angles Theorem. ## Question 2 Para el paso 6, la razón correspondiente es Substitution Property of Equality. ## Question 3 Para el paso 9, la razón correspondiente es Subtraction Property of Equality. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Geometric Proofs" ] }

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Question

Explanation:

Identificar la razón para el paso 2

Identificar la razón para el paso 6

Identificar la razón para el paso 9

Answer:

Question 1

Question 2

Question 3