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 Pythagorean Theorem?

Back

A mathematical principle stating 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

If two triangles are similar, what can be said about their corresponding sides?

Back

The lengths of their corresponding sides are proportional.

Front

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

Back

Use the ratio of the lengths of corresponding sides to set up a proportion and solve for the unknown length.

Front

What is the relationship between the angles of similar triangles?

Back

All corresponding angles are equal.

Front

How do you apply the Pythagorean Theorem to find the length of a side?

Back

Identify the lengths of the two shorter sides (a and b), square them, add the results, and take the square root to find the hypotenuse (c).

Front

What is the formula to calculate the diagonal of a rectangle?

Back

Diagonal (d) = √(length² + width²).

Front

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

Back

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

Front

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

Back

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