in similar triangles, the corresponding side lengths are ______.
triangles are ______ when their corresponding sides and angles are equal.
triangles are ______ when their corresponding angles are equal, and their sides are proportional.
the principle stating that corresponding sides of similar triangles are proportional is known as ______.
the congruence criterion that requires three pairs of corresponding sides to be equal is called ______.
the similarity criterion that requires two pairs of corresponding angles to be equal is called ______.
the theorem stating that the midsegment of a triangle is parallel to the third side and half its length is the ______ theorem.

Question

Accepted Answer

### 1. In similar triangles, the corresponding side lengths are ______.
# Brief Explanations:
Similar triangles have corresponding sides that are in proportion (or proportional). This is a key property of similar triangles, where the ratio of corresponding sides is constant.
# Answer:
proportional (or in proportion)

### 2. Triangles are ______ when their corresponding sides and angles are equal.
# Brief Explanations:
By definition, congruent triangles have all corresponding sides and angles equal. Congruence means the triangles are identical in shape and size.
# Answer:
congruent

### 3. Triangles are ______ when their corresponding angles are equal, and their sides are proportional.
# Brief Explanations:
The definition of similar triangles is that their corresponding angles are equal (equiangular) and corresponding sides are in proportion (proportional). This is the fundamental concept of similar triangles.
# Answer:
similar

### 4. The principle stating that corresponding sides of similar triangles are proportional is known as ______.
# Brief Explanations:
The Basic Proportionality Theorem (also known as Thales' theorem) or more directly, the property of similar triangles regarding proportional sides is often referred to as the "Proportionality of Similar Triangles" or the "SSS Similarity Criterion" (but more generally, the concept that corresponding sides of similar triangles are proportional is a core property, and the principle is often associated with the definition of similar triangles or the "Similar Triangles Proportionality Principle". However, the most specific term here is the "Basic Proportionality Theorem" in the context of triangle similarity, or more commonly, the property is part of the definition of similar triangles, but the principle is often called the "Proportionality of Similar Triangles" or the "Similar Triangles Proportionality Principle". Alternatively, the "SSS Similarity Criterion" relates to sides being proportional, but the general principle is that corresponding sides of similar triangles are proportional, which is a fundamental property.
# Answer:
Proportionality of Similar Triangles (or Basic Proportionality Theorem / Thales' Theorem in some contexts, or the Similar Triangles Proportionality Principle)

### 5. The congruence criterion that requires three pairs of corresponding sides to be equal is called ______.
# Brief Explanations:
In triangle congruence, the SSS (Side - Side - Side) congruence criterion states that if three pairs of corresponding sides of two triangles are equal, then the triangles are congruent.
# Answer:
SSS (Side - Side - Side) Congruence Criterion

### 6. The similarity criterion that requires two pairs of corresponding angles to be equal is called ______.
# Brief Explanations:
For triangle similarity, the AA (Angle - Angle) similarity criterion (also known as AAA similarity, since if two angles are equal, the third must be equal too) states that if two pairs of corresponding angles of two triangles are equal, the triangles are similar.
# Answer:
AA (Angle - Angle) Similarity Criterion (or AAA Similarity Criterion)

### 7. The theorem stating that the midsegment of a triangle is parallel to the third side and half its length is the ______ theorem.
# Brief Explanations:
The Midsegment Theorem (also known as the Midline Theorem) of a triangle states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.
# Answer:
Midsegment (or Midline)

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Question

Explanation:

1. In similar triangles, the corresponding side lengths are ______.

Answer:

2. Triangles are ______ when their corresponding sides and angles are equal.