Similar Triangles and Pythagorean Theorem

Front

What are similar triangles?

Back

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 AA criterion for triangle similarity?

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What is the SAS criterion for triangle similarity?

Back

If two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar.

Front

What is the SSS criterion for triangle similarity?

Back

If the three sides of one triangle are in proportion to the three sides of another triangle, the triangles are similar.

Front

What is the Pythagorean Theorem?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. (a² + b² = c²)

Front

How do you find the missing side in a right triangle using the Pythagorean Theorem?

Back

Rearrange the Pythagorean Theorem formula to solve for the missing side: c = √(a² + b²) or a = √(c² - b²) or b = √(c² - a²).

Front

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

Back

The corresponding angles of similar triangles are equal.

Front

If the sides of Triangle ABC are 3, 4, and 5, what are the sides of a similar triangle with a scale factor of 2?

Back

The sides of the similar triangle would be 6, 8, and 10.

Front

What is the relationship between the areas of two similar triangles?

Back

The ratio of their areas is equal to the square of the ratio of their corresponding sides.

Front

If Triangle ABC has angles of 30°, 60°, and 90°, what are the angles of a similar triangle?

Back

The angles of the similar triangle will also be 30°, 60°, and 90°.