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 in proportion.

Front

What does SSS stand for in triangle similarity?

Back

SSS stands for Side-Side-Side similarity. It states that if the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.

Front

What does SAS stand for in triangle similarity?

Back

SAS stands for Side-Angle-Side similarity. It states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What does AA stand for in triangle similarity?

Back

AA stands for Angle-Angle similarity. It states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

If ∆ABC ≅ ∆XYZ, what can we conclude about their corresponding sides?

Back

If ∆ABC is congruent to ∆XYZ, then their corresponding sides are equal in length.

Front

How can you determine if two triangles are similar using proportions?

Back

To determine if two triangles are similar using proportions, compare the ratios of the lengths of corresponding sides. If the ratios are equal, the triangles are similar.

Front

What is the significance of the corresponding angles in similar triangles?

Back

In similar triangles, corresponding angles are equal, which is a key criterion for establishing similarity.

Front

What is the relationship between the areas of similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Front

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

Back

Yes, triangle A and triangle B are similar because the sides are in proportion (3:6, 4:8, 5:10).

Front

What is the criteria for two triangles to be not similar?

Back

Two triangles are not similar if their corresponding angles are not equal or if the ratios of their corresponding sides are not equal.