Similar Triangles

Front

What is the AA~ postulate in similar triangles?

Back

The AA~ (Angle-Angle Similarity) postulate states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does the SAS~ postulate indicate?

Back

The SAS~ (Side-Angle-Side Similarity) postulate states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What is the SSS~ postulate?

Back

The SSS~ (Side-Side-Side Similarity) postulate states that if the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

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

Back

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

Front

How can you determine if two triangles are similar using SAS~?

Back

To determine if two triangles are similar using SAS~, check if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal.

Front

How can you determine if two triangles are similar using SSS~?

Back

To determine if two triangles are similar using SSS~, check if the ratios of the lengths of corresponding sides are equal.

Front

What is the significance of similar triangles in geometry?

Back

Similar triangles have the same shape but may differ in size. They maintain proportional relationships between corresponding sides and equal corresponding angles.

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 XYZ are 3, 4, and 5, and the sides of triangle PQR are 6, 8, and 10, are the triangles similar?

Back

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

Front

What is the relationship between the areas of two similar triangles?

Back

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