Question

f.) congruent - circe one: yes no if yes, then by __________ i.) congruent - circe one: yes no if yes, then by ________ c.) by hl → need: ________ f.) by sas → need: __________ i.) by aas → need: ∠a≅∠p

Explanation:

Step1: Analyze f) triangles

Check for congruence conditions. Triangles have two pairs of corresponding angles equal and one non - included side equal. So, by AAS (Angle - Angle - Side) they are congruent.

Step2: Analyze i) triangles

Check for congruence conditions. Triangles have three pairs of corresponding sides equal. So, by SSS (Side - Side - Side) they are congruent.

Step3: Analyze c) for HL

HL (Hypotenuse - Leg) requires the hypotenuse and one leg of a right - triangle to be congruent to the hypotenuse and one leg of another right - triangle. We need $DF\cong XV$ (hypotenuses) and $DE\cong VW$ (legs).

Step4: Analyze f) for SAS

SAS (Side - Angle - Side) requires two sides and the included angle to be congruent. We need $\angle E\cong\angle U$ (included angles) and $ED\cong UW$ and $EF\cong UV$ (sides).

Step5: Analyze i) for AAS

AAS requires two angles and a non - included side to be congruent. Given $\angle A\cong\angle P$ as stated, we also need another pair of angles and a non - included side to be congruent.

Answer:

f) Congruent - Circle one: Yes; If yes, then by AAS
i) Congruent - Circle one: Yes; If yes, then by SSS
c) By HL → need: Hypotenuse $DF\cong XV$ and leg $DE\cong VW$
f) By SAS → need: $\angle E\cong\angle U$, $ED\cong UW$, $EF\cong UV$
i) By AAS → need: $\angle A\cong\angle P$ and another pair of angles and non - included side congruent