Question

1. which of the following statements about the congruent triangles below is true?

options:

• $overline{bc} cong overline{ef}$
• $overline{ac} cong overline{de}$
• $overline{ac} cong overline{ef}$
• $overline{ab} cong overline{df}$

Explanation:

Step1: Match congruent marked sides

• $\overline{AB}$ (1 mark) $\cong \overline{DE}$ (1 mark)
• $\overline{BC}$ (2 marks) $\cong \overline{EF}$ (2 marks)
• $\overline{AC}$ (3 marks) $\cong \overline{DF}$ (3 marks)

Step2: Verify each option

1. $\overline{BC} \cong \overline{EF}$: Matches the 2-mark congruent sides.
2. $\overline{AC} \cong \overline{DE}$: $\overline{AC}$ (3 marks) and $\overline{DE}$ (1 mark) are not congruent.
3. $\overline{AC} \cong \overline{EF}$: $\overline{AC}$ (3 marks) and $\overline{EF}$ (2 marks) are not congruent.
4. $\overline{AB} \cong \overline{DF}$: $\overline{AB}$ (1 mark) and $\overline{DF}$ (3 marks) are not congruent.

Answer:

$\boldsymbol{\overline{BC} \cong \overline{EF}}$