Question

justus wants to explain why \\( \triangle a b c \cong \triangle a b d \\) using the sss congruence theorem. in his explanation, which sides will he say are congruent by the reflexive property of congruence?
option \\#1: \\( \overline{a b} \\) and \\( \overline{a b} \\)
option \\#2: \\( \overline{a c} \\) and \\( \overline{a c} \\)
option \\#3: \\( \overline{b c} \\) and \\( \overline{b d} \\)
option \\#4: \\( \overline{a d} \\) and \\( \overline{a d} \\)
option \\#5: \\( \overline{a c} \\) and \\( \overline{a d} \\)
(1 point)
justus will say that the sides listed in option \\# are congruent by the reflexive property of congruence.

Explanation:

Step1: Understand the reflexive property

The reflexive property of congruence states that any segment is congruent to itself.

Step2: Check each option

• Option #1: \(\overline{AB}\) is a common side in \(\triangle ABC\) and \(\triangle ABD\). By the reflexive property, \(\overline{AB}\cong\overline{AB}\).
• Option #2: \(\overline{AC}\) is not a common side in the two triangles \(\triangle ABC\) and \(\triangle ABD\) in the context of proving their congruence.
• Option #3: \(\overline{BC}\) and \(\overline{BD}\) are not the same segment. They are two different segments.
• Option #4: \(\overline{AD}\) is not a side of \(\triangle ABC\).
• Option #5: \(\overline{AC}\) and \(\overline{AD}\) are two different segments.

Answer:

Option #1