Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the relationship between two triangles that have the same shape but may differ in size. This means their corresponding angles are equal and their corresponding sides are proportional.

Front

What are the criteria for triangle similarity?

Back

The criteria for triangle similarity are: 1) AA (Angle-Angle) - If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2) SSS (Side-Side-Side) - If the corresponding sides of two triangles are proportional, the triangles are similar. 3) SAS (Side-Angle-Side) - If two sides of one triangle are proportional to two sides of another triangle and the included angle is equal, the triangles are similar.

Front

If two triangles are similar, what can be said about their corresponding sides?

Back

If two triangles are similar, the corresponding sides are proportional.

Front

What does AA stand for in triangle similarity?

Back

AA stands for Angle-Angle, which is a criterion for triangle similarity stating that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What does SSS stand for in triangle similarity?

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SSS stands for Side-Side-Side, which is a criterion for triangle similarity stating that if the corresponding sides of two triangles are proportional, the triangles are similar.

Front

What does SAS stand for in triangle similarity?

Back

SAS stands for Side-Angle-Side, which is a criterion for triangle similarity stating that if two sides of one triangle are proportional to two sides of another triangle and the included angle is equal, the triangles are similar.

Front

If triangle ABC is similar to triangle DEF, what can be said about their angles?

Back

If triangle ABC is similar to triangle DEF, then angle A = angle D, angle B = angle E, and angle C = angle F.

Front

If the sides of triangle ABC are 3, 4, and 5, and triangle DEF is similar to triangle ABC with a scale factor of 2, what are the lengths of the sides of triangle DEF?

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The lengths of the sides of triangle DEF are 6, 8, and 10.

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How can you determine if two triangles are similar using the AA criterion?

Back

To determine if two triangles are similar using the AA criterion, check if two angles of one triangle are equal to two angles of the other triangle.

Front

If triangle XYZ has sides of lengths 6, 8, and 10, and triangle PQR has sides of lengths 3, 4, and 5, are they similar?

Back

Yes, triangle XYZ and triangle PQR are similar because their corresponding sides are proportional (6:3, 8:4, 10:5).