Reasoning and proof
Lines, angles, and planes
Congruence
Triangles
Triangle
A triangle consists of three connected line segments, such that the line segments form a closed shape.
Congruence
Two triangles are congruent if all of the angles and sides of the two triangles are equal to each other.
Identity
We use the property of identity to say that an angle or a line segment is congruent to itself.
Pythagorean theorem
The square of the hypotenuse of a right triangle is equal to the sum of squares of its sides, given by
\begin{equation} c^2 = a^2 + b^2 \qquad \textnormal{(Pythagorean theorem)} \end{equation}This follows from the law of cosines.
Perimeter
The perimeter of a triangle is equal to the sum of its sides. That is,
\begin{equation} P = d + e + f \qquad \textnormal{(Perimeter)} \end{equation}where d, e, and f are the lengths of its sides.
Quadrilaterals
Quadrilateral
A quadrilateral consists of four connected line segments, such that the line segments form a closed shape.
Parallelogram
A parallelogram is a quadrilateral such that both of the opposite sides of the quadrilateral are parallel.
Altitude
An altitude of a parallelogram is a line from a vertex to a line segment on the other side of the parallelogram, such that the altitude and the line segment form a perpendicular angle.
Kite
A kite is a quadrilateral with two pairs of adjacent congruent sides, and no more than two sides are congruent.