1. triangles are considered similar if their corresponding angles are ________.
2. similar triangles have corresponding sides that are ________.
3. the criterion that determines triangle similarity based on two pairs of congruent angles is called ________ criterion.
4. the criterion that determines triangle similarity based on all three pairs of corresponding sides being proportional is called ________ criterion.
5. the criterion that determines triangle similarity based on two proportional sides and a congruent included angle is called ________ criterion.
6. if two triangles have congruent corresponding angles and their sides are proportional, the triangles are considered ________.
7. in the aa criterion, once two pairs of angles are congruent, the ________ pair of angles will also be congruent.

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Accepted Answer

### Question 1:
# Brief Explanations:
By the definition of similar triangles, corresponding angles must be congruent (equal) for triangles to be similar.
# Answer:
congruent (or equal)

### Question 2:
# Brief Explanations:
Similar triangles have corresponding sides that are proportional. This is a key property of similar triangles, meaning the ratios of corresponding sides are equal.
# Answer:
proportional

### Question 3:
# Brief Explanations:
The criterion for triangle similarity with two pairs of congruent angles is the AA (Angle - Angle) criterion. Since the sum of angles in a triangle is fixed, two congruent angles imply the third is also congruent, so two pairs are enough to establish similarity.
# Answer:
AA (Angle - Angle)

### Question 4:
# Brief Explanations:
When all three pairs of corresponding sides of triangles are proportional, the criterion for similarity is SSS (Side - Side - Side) similarity criterion, analogous to the SSS congruence criterion but for similarity (proportional sides instead of equal sides).
# Answer:
SSS (Side - Side - Side)

### Question 5:
# Brief Explanations:
The criterion for triangle similarity with two proportional sides and a congruent included angle is the SAS (Side - Angle - Side) similarity criterion, similar to the SAS congruence criterion but with proportional sides.
# Answer:
SAS (Side - Angle - Side)

### Question 6:
# Brief Explanations:
If two triangles have congruent corresponding angles and proportional sides, by the definition of similar triangles, they are similar. This combines the angle and side properties of similar triangles.
# Answer:
similar

### Question 7:
# Brief Explanations:
In a triangle, the sum of interior angles is $180^{\circ}$. In the AA criterion, if two pairs of angles are congruent, let the angles of the first triangle be $A_1,B_1,C_1$ and the second be $A_2,B_2,C_2$. If $A_1 = A_2$ and $B_1=B_2$, then $C_1=180 - A_1 - B_1$ and $C_2 = 180 - A_2 - B_2=180 - A_1 - B_1$, so the third pair of angles is also congruent.
# Answer:
third

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