Question

select the correct answer from each drop - down menu.
the condition drop - down menu proves that $\triangle abc$ and $\triangle efg$ are congruent by the sas criterion.
if $ab\
eq ef$, thdrop - down menuency is violated. in this situation, angle $c$ drop - down menu angle $g$.
drop - down menu options for the first blank: angle $a$ is congruent to angle $e$, angle $b$ is congruent to angle $f$, $ab = ef$, angle $c$ is congruent to angle $g$
buttons: reset, next

Explanation:

Step1: Recall SAS congruence rule

SAS (Side-Angle-Side) requires two pairs of congruent sides, with the included angle congruent between them. From the diagram: $AC \cong EG$, $BC \cong FG$. The included angle for $\triangle ABC$ is $\angle C$, for $\triangle EFG$ is $\angle G$. Wait, no—correction: for sides $AC, BC$ the included angle is $\angle C$; for $EG, FG$ included angle is $\angle G$. But wait, the first blank needs the condition for SAS. Wait, recheck: the marked sides: $AC$ (one tick) $\cong EG$ (one tick), $BC$ (two ticks) $\cong FG$ (two ticks). So the included angles are $\angle C$ and $\angle G$? No, wait no: SAS is side-included angle-side. So if we have $AC \cong EG$, $BC \cong FG$, the included angle is $\angle C$ (between $AC$ and $BC$) and $\angle G$ (between $EG$ and $FG$). But wait the first dropdown: the options are angle A≅E, angle B≅F, AB=EF, angle C≅G. Wait no, wait I misread: the sides: $AB$ is unmarked, $EF$ unmarked; $AC$ and $EG$ have one tick, $BC$ and $FG$ have two ticks. So for SAS, we need the angle between the two marked sides to be congruent. The angle between $AC$ and $BC$ is $\angle C$, between $EG$ and $FG$ is $\angle G$. But wait, the second part: if $AB
eq EF$, then congruency is violated, so angle C is **not congruent** to angle G? No, wait no: first, the first blank: which condition proves SAS? Wait no, wait maybe I mixed up the sides. Wait, maybe the sides are $AB$ and $EF$? No, the marked sides are $AC \cong EG$, $BC \cong FG$. So SAS requires $\angle C \cong \angle G$. But wait the first dropdown: option 4 is angle C≅G. But wait, no, wait the question says "the condition ____ proves that $\triangle ABC$ and $\triangle EFG$ are congruent by SAS".

Wait, let's re-express SAS properly: For $\triangle ABC \cong \triangle EFG$ by SAS, we need:

1. One pair of sides congruent: $AC \cong EG$ (given by tick marks)
2. The included angle congruent: $\angle C \cong \angle G$
3. The other adjacent side congruent: $BC \cong FG$ (given by tick marks)

So the missing condition for SAS is $\angle C \cong \angle G$.

Now the second part: If $AB
eq EF$, then the triangles are not congruent, so $\angle C
cong \angle G$ (angle C is not congruent to angle G).

Wait but let's confirm the first dropdown: the options are:

• angle A is congruent to angle E
• angle B is congruent to angle F
• AB = EF
• angle C is congruent to angle G

Yes, the SAS condition requires the included angle between the two marked sides, which is $\angle C \cong \angle G$.

Then, if $AB
eq EF$, the triangles can't be congruent, so the congruence of $\angle C$ and $\angle G$ is violated, meaning $\angle C$ is **not congruent to** $\angle G$.

Step2: Match to dropdown options

First blank: select "angle C is congruent to angle G"
Second blank: "is not congruent to"

Answer:

1. The condition: angle C is congruent to angle G proves that $\triangle ABC$ and $\triangle EFG$ are congruent by the SAS criterion.
2. If $AB

eq EF$, the congruency is violated. In this situation, angle C is not congruent to angle G.