Similar Triangles and the Walking Dead

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 is the Angle-Angle (AA) criterion for similarity?

Back

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

Front

What is the Side-Side-Side (SSS) criterion for similarity?

Back

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

Front

What is the Side-Angle-Side (SAS) criterion for similarity?

Back

The Side-Angle-Side (SAS) criterion states that if one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in proportion, then the triangles are similar.

Front

If two triangles are similar, what can be said about their corresponding sides?

Back

The lengths of their corresponding sides are proportional.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 6 cm and side DE is 9 cm, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 6:9 or 2:3.

Front

How do you find the height of a tree using similar triangles?

Back

You can use the properties of similar triangles to set up a proportion between the height of the tree and the length of its shadow compared to a smaller object with a known height and shadow length.

Front

If a tree casts a shadow of 12 ft and a 5 ft person casts a shadow of 3 ft, what is the height of the tree?

Back

Using the proportion: height of tree / 12 ft = 5 ft / 3 ft, the height of the tree is 20 ft.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If two triangles have angles measuring 30°, 60°, and 90°, are they similar?

Back

Yes, because they have the same angle measures.