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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 congruent according to the LLL criterion.
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent according to the LLL criterion.
True (A)
Two figures are similar if their corresponding sides are congruent and their corresponding angles are proportional.
Two figures are similar if their corresponding sides are congruent and their corresponding angles are proportional.
False (B)
The AIA theorem states that if two angles and a side of one triangle are congruent to two angles of another triangle, the triangles are congruent.
The AIA theorem states that if two angles and a side of one triangle are congruent to two angles of another triangle, the triangles are congruent.
True (A)
Congruence of triangles can be established only through the comparison of angles.
Congruence of triangles can be established only through the comparison of angles.
There must be a correspondence between the sides of two similar figures.
There must be a correspondence between the sides of two similar figures.
Flashcards
Side-Side-Side (SSS) Congruence
Side-Side-Side (SSS) Congruence
If all three sides of one triangle are the same length as the three sides of another triangle, the two triangles are congruent.
Similarity Conditions
Similarity Conditions
Figures are similar if their corresponding angles are congruent (equal) and their corresponding sides are proportional (in the same ratio).
Angle-Side-Angle (ASA) Congruence
Angle-Side-Angle (ASA) Congruence
The ASA postulate states that if two angles and the included side (the side between the angles) of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Triangle Congruence
Triangle Congruence
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Corresponding Sides
Corresponding Sides
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Study Notes
Congruent Triangles
- Side-Side-Side (SSS): Two triangles are congruent if all three sides of one triangle are equal in length to the corresponding three sides of the other triangle.
- Side-Angle-Angle (SAA): Two triangles are congruent if one side and two angles of one triangle are equal to the corresponding side and two angles of the other triangle.
- Angle-Angle-Side (AAS): Two triangles are congruent if two angles and one side of one triangle are equal to the corresponding two angles and one side of the other triangle.
Similar Triangles
- Similarity: Two figures are similar if their corresponding angles are equal in measure and their corresponding sides are proportional.
- Side-Side-Side (SSS): Two triangles are similar if their corresponding sides are proportional.
- Side-Angle-Side (SAS): Two triangles are similar if two sides of one triangle are proportional to two sides of another triangle and the included angle is congruent.
- Angle-Angle (AA): Two triangles are similar if two angles of one triangle are congruent to two angles of another triangle.
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