Given parallelogram ABCD with bisectors of angles A and D intersecting at point E, and the distance from E to AD measuring 10 units, determine the distance from A to CD in units.
|Concept||Definition||Theorem / Comment|
|Triangle||A polygon with three sides and three angles.||The sum of the angles in a triangle is 180 degrees.|
|Parallelogram||A parallelogram is a quadrilateral with both pairs of opposite sides parallel.||Opposite sides of a parallelogram are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other.|
|Angle bisector||A line or ray that divides an angle into two congruent angles..||The Angle Bisector Equidistant Theorem states that if a point lies on the angle bisector of an angle, then it is equidistant from the two sides of the angle.|
|Parallel lines||Two lines in a plane that do not intersect.||If two parallel lines are cut by a transversal, then the alternate interior angles are congruent, the corresponding angles are congruent, and the consecutive interior angles are supplementary.|
|Distance||The distance between two geometric figures is generally defined as the minimum distance between any two points, one on each of the two figures..|
|Perpendicular lines||Two lines or line segments that intersect at a right angle.||Two lines perpendicular to a same line are parallel to each other.|
|Rectangle||A rectangle is a two-dimensional shape with four straight sides and four right angles (90-degree angles).||In a rectangle, opposite sides are congruent and parallel.|
|Congruence||Two triangles are said to be congruent if all corresponding sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle..||There are several ways to prove that two triangles are congruent, including the Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Hypotenuse-Leg (HL) criteria.|
|Auxiliary line||Auxiliary line is a line that is added to a diagram in order to help prove a theorem or solve a problem.||Often, an auxiliary line is drawn to create additional congruent or similar triangles, to create parallel lines, or to create right angles. The use of auxiliary lines can simplify a problem or make a proof more straightforward. However, it is important to ensure that the auxiliary line does not create any new intersections or angles that were not present in the original diagram.|
Amidst the lines and angles that we see,
A challenge awaits, a geometry mystery,
Mastering problem-solving, the key,
To unlock the secrets of symmetry.
A parallelogram, ABCD its name,
Bisectors and distances, the tools to claim,
Find the distance from A to CD,
With precision and skill, solve it with glee.
A journey of discovery, a quest to prevail,
With logic and reasoning, let us unveil,
The distance between two sides we seek,
A problem to solve, a victory to keep.
So take on the challenge, with courage and might,
As we journey together, towards problem-solving light,
Master geometry, unleash your potential,
With bisectors and distances, make the problem incidental.
If you're interested in finding more poems with a focus on geometry, you may enjoy this collection: More geometry thematic poems.