Question

1. state what information is needed in order to make the given congruent reason true.

sas

1. state what information is needed in order to make the given congruent reason true

aas

1. state what information is needed in order to make the given congruent reason true.

asa

1. state what information is needed in order to make the given congruent reason true

sas

1. state what information is needed in order to make the given congruent reason true.

asa

1. state what information is needed in order to make the given congruent reason true.

sas

1. state what information is needed in order to make the given congruent reason true.

asa

1. state what information is needed in order to make the given congruent reason true

asa

Explanation:

For each question, we use the definition of the given triangle congruence criterion to identify the missing corresponding congruent sides/angles:

1. SAS (Side-Angle-Side): Requires two pairs of corresponding sides congruent, with the included angle congruent.
2. AAS (Angle-Angle-Side): Requires two pairs of corresponding angles congruent, with a non-included corresponding side congruent.
3. ASA (Angle-Side-Angle): Requires two pairs of corresponding angles congruent, with the included side congruent.

Answer:

1. $DC \cong XW$ (the other pair of included sides for SAS)
2. $\angle EGF \cong \angle TFG$ (second pair of corresponding angles for AAS, alongside $\angle EFG \cong \angle TGF$ and $FG \cong GF$)
3. $\angle F \cong \angle C$ (second pair of corresponding angles for ASA, alongside $\angle DBF \cong \angle ABC$ and $DB \cong AB$)
4. $EF \cong ED$ (the other pair of included sides for SAS, alongside $\angle CEF \cong \angle DEF$ and $CF \cong DF$)
5. $BC \cong RS$ (the included side for ASA, alongside $\angle C \cong \angle R$ and $\angle B \cong \angle Q$)
6. $\angle N \cong \angle P$ (the included angle for SAS, alongside $NK \cong PM$ and $NA \cong PA$)
7. $BC \cong CB$ is shared, so we need $\angle ICB \cong \angle DBC$ (second pair of corresponding angles for ASA, alongside $\angle IBC \cong \angle DCB$)
8. $\angle H \cong \angle M$ (second pair of corresponding angles for ASA, alongside $\angle HIL \cong \angle MKI$ and $HI \cong MK$)