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

State the AA (Angle-Angle) similarity postulate.

Back

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

Front

State the SSS (Side-Side-Side) similarity postulate.

Back

If the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

State the SAS (Side-Angle-Side) similarity postulate.

Back

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

What is the Pythagorean Theorem?

Back

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

Front

If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

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

Back

Use the ratio of the lengths of corresponding sides. If triangle A is similar to triangle B, then A's side length / B's side length = k (a constant ratio).

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 sides in the ratio 2:3, what can be said about their areas?

Back

The ratio of their areas will be (2:3)² = 4:9.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.