Misc Geometry ACT Review

Front

What is the formula for finding the coordinates of a point that divides a line segment in a given ratio?

Back

If point B divides line segment AC in the ratio m:n, then the coordinates of B are given by: \( B = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \) where A(x1, y1) and C(x2, y2).

Front

What is the distance formula in a coordinate plane?

Back

The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Front

What is the definition of similar triangles?

Back

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

Front

How do you find the hypotenuse of a right triangle using the Pythagorean theorem?

Back

In a right triangle with legs a and b, the hypotenuse c is found using: \( c = \sqrt{a^2 + b^2} \).

Front

What is the sine of an angle in a right triangle?

Back

The sine of angle A is defined as the ratio of the length of the opposite side to the length of the hypotenuse: \( \sin A = \frac{\text{opposite}}{\text{hypotenuse}} \).

Front

What is the midpoint formula in a coordinate plane?

Back

The midpoint M of a line segment with endpoints A(x1, y1) and B(x2, y2) is given by: \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).

Front

What is the relationship between the sides of similar triangles?

Back

The lengths of corresponding sides of similar triangles are proportional. If the ratio of the sides is a:b, then the ratio of the areas is a^2:b^2.

Front

How do you calculate the length of a side in a triangle using the sine rule?

Back

In any triangle, the ratio of a side to the sine of its opposite angle is constant: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \).

Front

What is the formula for the area of a triangle?

Back

The area A of a triangle can be calculated using: \( A = \frac{1}{2} \times \text{base} \times \text{height} \).

Front

What is the definition of a right triangle?

Back

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