Question

# If in $\triangle \mathrm{A B C}$ and $\triangle \mathrm{D E F}$, AB = DE, $\mathrm{m} \angle \mathrm{A B C=\mathrm{m} \angle E D F}$, BC = DF, $\mathrm{A C}=(20 x-10)$, and $\mathrm{E F}=(15 x+15)$, what is the value of x?

Solution

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\begin{align*} & \underline{ \text{Statements}} && \underline{\text{Reasons}} \\\\ & 1.\quad AB=DE; BC=DF ; \ m\angle ABC=m\angle EDF && \text{{\color{#c34632}1. \quad Given}} \\\\ & 2.\quad \overline{AB} \cong \overline{DE}, \overline{BC} \cong \overline{DF} && \text{{\color{#c34632}2. \quad definition of congruent sides}} \\\\ & 3.\quad \angle ABC \cong \angle EDF && \text{{\color{#c34632}3. \quad definition of congruent angles }} \\\\ & 4.\quad \triangle ABC \cong \triangle EDF && \text{{\color{#c34632}4. \quad SAS postulate}} \\\\ &5. \quad \overline{AC} \cong \overline{EF} && \text{{\color{#c34632}5. \quad CPCTC \ Corresponding parts of }}\\\\ & && \quad \quad \text{{\color{#c34632}congruent triangles are congruent}}\\\\ \end{align*}

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