Similarity

Front

What does SAS stand for in triangle similarity?

Back

SAS stands for Side-Angle-Side, a criterion for triangle similarity where two sides of one triangle are proportional to two sides of another triangle, and the included angle is equal.

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 proportional.

Front

How do you determine if two triangles are similar using the AAS criterion?

Back

AAS stands for Angle-Angle-Side. If two angles of one triangle are equal to two angles of another triangle and the side between them is proportional, the triangles are similar.

Front

What is the relationship between the sides of similar triangles?

Back

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

Front

If triangle ABC is similar to triangle DEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

DF = 12. The ratio of sides AB to DE is 4:8, which simplifies to 1:2. Therefore, the corresponding side DF must be twice the length of AC.

Front

What is the definition of the ASA criterion for triangle similarity?

Back

ASA stands for Angle-Side-Angle. If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are similar.

Front

How can you find a missing side in similar triangles?

Back

To find a missing side in similar triangles, set up a proportion using the lengths of the corresponding sides and solve for the unknown.

Front

What does the SSS criterion for triangle similarity state?

Back

SSS stands for Side-Side-Side. If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

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

Back

Yes, they are similar because they have the same angle measures.

Front

What is the height of a tree if it casts a shadow of 10 meters and a 2-meter tall person casts a shadow of 5 meters?

Back

The height of the tree is 20 meters, using the property of similar triangles.