Right Triangle Similarity

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

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): a² + b² = c².

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if they have the same shape, which means their corresponding angles are equal and their corresponding sides are in proportion.

Front

How can you determine if two triangles are similar using angle-angle (AA) similarity?

Back

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

Front

What is the ratio of the sides in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the sides are in the ratio 1:√3:2.

Front

What is the ratio of the sides in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the sides are in the ratio 1:1:√2.

Front

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

Back

To find the length of a side in a similar triangle, set up a proportion using the lengths of corresponding sides from the two triangles.

Front

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

Back

The ratio of their corresponding sides is 1:2.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for applying the Pythagorean theorem.

Front

How can you use the Pythagorean theorem to find a missing side in a right triangle?

Back

To find a missing side, rearrange the Pythagorean theorem formula: c² = a² + b², and solve for the unknown side.