Pythagorean Theorem and Similarity Review

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that 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). It can be expressed as: a² + b² = c².

Front

What are similar triangles?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if: 1. All pairs of corresponding angles are congruent. 2. The ratios of the lengths of corresponding sides are equal.

Front

If triangle ABC is similar to triangle DEF, and the lengths of AB and DE are 4 cm and 8 cm respectively, what is the ratio of their corresponding sides?

Back

The ratio of the corresponding sides is 1:2.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 ft.

Front

What is the relationship between the angles of similar triangles?

Back

In similar triangles, corresponding angles are equal.

Front

If two triangles have sides in the ratio 3:5, what can be said about their similarity?

Back

If the corresponding angles are also equal, then the triangles are similar.

Front

What is the significance of the 45-45-90 triangle?

Back

In a 45-45-90 triangle, the legs are equal in length, and the hypotenuse is √2 times the length of each leg.

Front

What is the significance of the 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where the side opposite the 30° angle is the shortest.