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): c² = a² + b².

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 relationship between the sides of similar triangles?

Back

The ratios of the lengths of corresponding sides of similar triangles are equal.

Front

If two right triangles are similar, how do their areas compare?

Back

The areas of similar triangles are proportional to the square of the lengths of their corresponding sides.

Front

What is the formula for the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

Front

If the sides of a right triangle are in the ratio 3:4:5, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem (3² + 4² = 5²).

Front

How do you find the length of a side in a right triangle using similarity?

Back

If two right triangles are similar, you can set up a proportion using the lengths of corresponding sides to find the unknown length.

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 in applying the Pythagorean theorem.