Triangle Similarity/Parallel Lines and Proportional Parts

Front

What is Triangle Similarity?

Back

Triangle similarity occurs when two triangles have the same shape but not necessarily the same size. This can be established through criteria such as AA (Angle-Angle), SSS (Side-Side-Side), or SAS (Side-Angle-Side).

Front

Define AA similarity criterion.

Back

AA similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

Define SSS similarity criterion.

Back

SSS similarity criterion states that if the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

Define SAS similarity criterion.

Back

SAS similarity criterion 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 does it mean if two triangles are not similar?

Back

If two triangles are not similar, it means they do not have the same shape, which can be due to differing angles or side lengths.

Front

If two triangles have angles measuring 30°, 60°, and 90°, what can be said about their similarity?

Back

If two triangles have angles measuring 30°, 60°, and 90°, they are similar by the AA criterion.

Front

How do you find the height of an object using similar triangles?

Back

To find the height of an object using similar triangles, set up a proportion between the heights and shadow lengths of the objects.

Front

What is the relationship between parallel lines and proportional parts?

Back

When a set of parallel lines intersects two transversals, the segments created on the transversals are proportional.

Front

If a road sign casts a shadow of 25 ft and is 20 ft tall, what is the ratio of height to shadow length?

Back

The ratio of height to shadow length is 20:25, which simplifies to 4:5.

Front

If the width of square J is 28 in and the ratio of widths of square J to square M is 4:5, what is the width of square M?

Back

The width of square M is 35 in.