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 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: c² = a² + b².

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 the diagonal of a rectangle?

Back

Use the Pythagorean Theorem: diagonal² = length² + width².

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 10 cm and side DE is 5 cm, what is the ratio of their sides?

Back

The ratio of their sides is 10:5 or 2:1.

Front

Find the length of the missing side in a right triangle where one side is 3 cm and the other side is 4 cm.

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5 cm.

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.

Front

If a television screen is 3 feet tall and 6 feet wide, how do you find the diagonal?

Back

Use the Pythagorean Theorem: diagonal² = 3² + 6²; diagonal² = 9 + 36; diagonal = √45 ≈ 6.7 feet.