Question

using angle - angle - side congruence theorem. what additional information could be used to prove △efg≅△efg using aas? choose three correct answers. (overline{eg}congoverline{eg}), (fg = 15) and (fg=15), (mangle42^{circ}) and (mangle g = 42^{circ}), (ef = 10) and (ef=12)

Explanation:

Step1: Recall AAS congruence

AAS (Angle - Angle - Side) requires two pairs of congruent angles and a non - included side congruent.

Step2: Analyze first option

$\overline{EG}\cong\overline{E'G'}$ gives a non - included side congruence which can be used with the two given pairs of angles for AAS.

Step3: Analyze second option

$FG = 15$ and $F'G'=15$ means $\overline{FG}\cong\overline{F'G'}$ which is a non - included side congruence and can be used for AAS.

Step4: Analyze third option

$m\angle G = 42^{\circ}$ and $m\angle G'=42^{\circ}$ gives another pair of congruent angles which can be used with the existing angle pairs and a non - included side for AAS.

Step5: Analyze fourth option

$EF = 10$ and $E'F'=12$ means $\overline{EF}
ot\cong\overline{E'F'}$, so it cannot be used for AAS.

Answer:

$\overline{EG}\cong\overline{E'G'}$, $FG = 15$ and $F'G'=15$, $m\angle G = 42^{\circ}$ and $m\angle G'=42^{\circ}$