Similar Triangles Flashcard

Front

What are similar triangles?

Back

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

Front

What is the criteria for triangles to be similar?

Back

Triangles are similar if they satisfy any of the following criteria: 1) AA (Angle-Angle) Criterion: If two angles of one triangle are equal to two angles of another triangle. 2) SSS (Side-Side-Side) Criterion: If the lengths of corresponding sides of two triangles are proportional. 3) SAS (Side-Angle-Side) Criterion: If two sides of one triangle are proportional to two sides of another triangle, and the included angles are equal.

Front

How do you find the length of a side in similar triangles?

Back

To find the length of a side in similar triangles, set up a proportion using the lengths of corresponding sides. For example, if triangle ABC is similar to triangle DEF, then (AB/DE) = (AC/DF) = (BC/EF). You can solve for the unknown side using cross-multiplication.

Front

What is the relationship between corresponding angles in similar triangles?

Back

In similar triangles, corresponding angles are congruent, meaning they have the same measure.

Front

If triangle RST is similar to triangle RVW, and the length of side RS is 6 mm and side RV is 9 mm, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 6:9, which simplifies to 2:3.

Front

What is the significance of the AA criterion in proving triangle similarity?

Back

The AA criterion is significant because it allows us to prove that two triangles are similar by showing that two pairs of corresponding angles are equal, without needing to know the lengths of the sides.

Front

How can you use similar triangles to solve real-world problems?

Back

Similar triangles can be used in real-world problems to find distances, heights, and lengths that are difficult to measure directly by creating proportional relationships based on known measurements.

Front

What is the scale factor in similar triangles?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar triangles. It indicates how much larger or smaller one triangle is compared to the other.

Front

If two triangles are similar and the length of one side of the first triangle is 10 cm, and the corresponding side of the second triangle is 15 cm, what is the scale factor?

Back

The scale factor is 10:15, which simplifies to 2:3.

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 side lengths.