Question

1. suppose △abc≅△efg. for each of the following, name the corresponding part. a. ∠a b. ∠bca c. (overline{ac}) d. ∠f e. ∠gef f. (overline{ge}) 4. suppose △aeb≅△dec. which angle in △dec corresponds to ∠abe? 5. if congruent, state the congruence postulate, sss, sas, asa, aas, or hl. if not, write

ot enough info\. 6. 7. 8. 9.

Explanation:

Step1: Recall congruent - triangle properties

When $\triangle ABC\cong\triangle EFG$, corresponding parts are equal.

Step2: Find corresponding angles and sides for $\triangle ABC\cong\triangle EFG$

a. $\angle A$ corresponds to $\angle E$.
b. $\angle BCA$ corresponds to $\angle FGE$.
c. $\overline{AC}$ corresponds to $\overline{EG}$.
d. $\angle F$ corresponds to $\angle B$.
e. $\angle GEF$ corresponds to $\angle CAB$.
f. $\overline{GE}$ corresponds to $\overline{CA}$.

Step3: For $\triangle AEB\cong\triangle DEC$

The angle in $\triangle DEC$ that corresponds to $\angle ABE$ is $\angle DCE$.

Step4: Analyze congruence postulates for given triangles

1. There are three pairs of equal sides. So, by SSS (Side - Side - Side) postulate, the two triangles are congruent.
2. There are two pairs of equal sides and the included angles are equal. So, by SAS (Side - Angle - Side) postulate, the two triangles are congruent.
3. There are two pairs of equal sides, but we don't know about the included angles. So, not enough info.
4. There are two pairs of equal angles and a pair of non - included equal sides. So, by AAS (Angle - Angle - Side) postulate, the two triangles are congruent.
5. There are two pairs of equal angles and the included side is equal. So, by ASA (Angle - Side - Angle) postulate, the two triangles are congruent.

Answer:

3.
a. $\angle E$
b. $\angle FGE$
c. $\overline{EG}$
d. $\angle B$
e. $\angle CAB$
f. $\overline{CA}$

1. $\angle DCE$
2. SSS
3. SAS
4. not enough info
5. AAS
6. ASA