Geometry Benchmark

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and the non-included side of one triangle are equal to the corresponding parts of another triangle.

Front

What is a scalene triangle?

Back

A scalene triangle is a triangle in which all three sides are of different lengths and all three angles are of different measures.

Front

How do you calculate the distance between two points in a coordinate plane?

Back

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

Front

What is the result of rotating a point (x, y) 90° counterclockwise about the origin?

Back

The coordinates of the point (x, y) after a 90° counterclockwise rotation about the origin become (-y, x).

Front

What is an acute isosceles triangle?

Back

An acute isosceles triangle is a triangle that has two equal sides and all three angles are less than 90 degrees.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are equal to the corresponding parts of another triangle.

Front

What is the definition of an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle measuring more than 90 degrees.

Front

How do you identify the type of triangle based on its sides?

Back

Triangles can be classified as scalene (all sides different), isosceles (two sides equal), or equilateral (all sides equal).

Front

What is the formula for the area of a triangle?

Back

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

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): \\( c^2 = a^2 + b^2 \\).