THS Geo FA2024 Similar Triangles

Front

What is the definition of similar triangles?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What does the AA~ postulate state?

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 SSS~ postulate state?

Back

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

Front

What does the SAS~ postulate state?

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

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

Back

The corresponding angles of triangle ABC and triangle DEF are equal.

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 their corresponding sides are in proportion (3:6, 4:8, 5:10).

Front

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

Back

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

Front

What is the relationship between the ratios of the sides of similar triangles?

Back

The ratios of the corresponding sides of similar triangles are equal.

Front

If triangle GHI has sides of lengths 5, 12, and 13, and triangle JKL has sides of lengths 10, 24, and 26, are they similar?

Back

Yes, triangle GHI and triangle JKL are similar because their corresponding sides are in proportion (5:10, 12:24, 13:26).

Front

What is the significance of the included angle in the SAS~ postulate?

Back

The included angle in the SAS~ postulate must be equal for the triangles to be considered similar.