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Questions and Answers
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are similar.
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are similar.
False (B)
Two figures are similar if their corresponding angles are congruent and their corresponding sides are proportional.
Two figures are similar if their corresponding angles are congruent and their corresponding sides are proportional.
True (A)
The AIA criterion states that if two angles and a side of one triangle are congruent to two angles of another triangle, then the triangles are congruent.
The AIA criterion states that if two angles and a side of one triangle are congruent to two angles of another triangle, then the triangles are congruent.
True (A)
The LLA criterion requires three sides to be congruent in order to determine triangle congruence.
The LLA criterion requires three sides to be congruent in order to determine triangle congruence.
There is no relationship between proportion and similarity in geometric figures.
There is no relationship between proportion and similarity in geometric figures.
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Study Notes
Congruence Criteria
- Side-Side-Side (SSS): Two triangles are congruent if all three sides of one triangle are congruent to all three sides of the other triangle.
- Side-Angle-Angle (SAA): Two triangles are congruent if one side and two angles of one triangle are congruent to one side and two angles of the other triangle.
- Angle-Angle-Side (AAS): Two triangles are congruent if two angles and a side of one triangle are congruent to two angles and a side of the other triangle.
Similarity
- Similarity: Two figures are similar if their corresponding angles are congruent and their corresponding sides are proportional.
- Corresponding Sides: When two figures are similar, their corresponding sides are proportional. This means that the ratio of the lengths of corresponding sides is the same.
- Corresponding Angles: When two figures are similar, their corresponding angles are congruent. This means that the angles have the same measure.
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