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). Formula: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

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

Back

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

Front

What is similarity in triangles?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

How can you determine if two triangles are similar?

Back

You can determine if two triangles are similar by checking if their angles are equal (Angle-Angle criterion) or if the sides are in proportion (Side-Side-Side criterion).

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 two triangles are similar and the length of one side of the first triangle is 6 cm and the corresponding side of the second triangle is 9 cm, what is the scale factor?

Back

The scale factor is 3:2 (9 cm / 6 cm = 1.5).

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

In a right triangle, if one leg is 12 units and the hypotenuse is 13 units, what is the length of the other leg?

Back

5 units (using the Pythagorean Theorem: 12² + b² = 13²; 144 + b² = 169; b² = 25; b = 5).

Front

What is the significance of the 3-4-5 triangle?

Back

The 3-4-5 triangle is a common example of a right triangle that satisfies the Pythagorean Theorem (3² + 4² = 5²).