Flashcard-Lessons 2.6 - 2.8

Front

What are the conditions for a set of lengths to form a right triangle?

Back

The lengths must satisfy the Pythagorean theorem: a^2 + b^2 = c^2, where c is the longest side.

Front

What does it mean for two triangles to be similar?

Back

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

Front

How do you calculate the height of a tree if it breaks at a certain height and you know the total height?

Back

Subtract the height at which the tree broke from the total height to find the height of the tree.

Front

What is the relationship between corresponding angles in similar figures?

Back

The corresponding angles in similar figures are congruent.

Front

How do you find a point that divides a line segment in a given ratio?

Back

Use the section formula: If A(x1, y1) and B(x2, y2) are points, and the ratio is m:n, then P(x, y) = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Front

What is a similarity statement in geometry?

Back

A similarity statement indicates that two figures are similar, typically written as ΔABC ~ ΔDEF.

Front

How do 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, the triangles are similar.

Front

What is the formula for finding the distance between two points in a coordinate plane?

Back

The distance d between two points (x1, y1) and (x2, y2) is given by d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the significance of congruent angles in similar triangles?

Back

Congruent angles ensure that the triangles maintain the same shape, which is essential for similarity.