Math

Math is an amazing subject I always look forward to every day. We are beginning to learn about points, lines, and planes; these 3 objects define how we live and how engineers build structures. There are formulas that find the distance between two points on a plane and the midpoint between two points on a plane. The reason I enjoy math is because if your answer is mathematically right, one cannot argue against it — there is proof it’s correct, unlike subjects like English where it’s based on opinions and sources like the New York Times.

One big project I am really proud of is the geometry portfolio I created in HTML and CSS. You can find the link to it here:

Geometry Portfolio

What is Geometry?

Geometry is the study of shapes, lines, and space. It starts with three basic ideas — points, lines, and planes — which we accept without formal definition. A point represents a location, a line extends infinitely in both directions, and a plane is a flat surface stretching forever. Using proper notation and clear labeling is key to avoiding mistakes.

Segments and Midpoints

A segment is a finite piece of a line with two endpoints. If point B lies between points A and C, the Segment Addition Postulate tells us AB + BC = AC. Congruent segments have equal lengths (≅), and a segment bisector passes through the midpoint of a segment.

Distance Between Points

The distance formula calculates how far apart two points are:
d = √((x₂ − x₁)² + (y₂ − y₁)²)
The midpoint formula finds the center of a segment:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Angles and Their Relationships

Angles are formed by two rays sharing a common endpoint (vertex). Angles can be acute, right, obtuse, or straight. The Angle Addition Postulate states that if a point lies inside an angle, the sum of the two smaller angles equals the whole angle. Understanding complementary, supplementary, vertical, and linear pair angles helps solve problems and proofs.

Key Takeaways

• Label diagrams clearly: points, lines, planes, segments, and angles.
• Use the Segment Addition Postulate: AB + BC = AC when B is between A and C.
• Distance and midpoint formulas allow calculation of lengths and centers of segments.
• Angles can be classified and added using the Angle Addition Postulate.
• Vertical and linear pair angles have predictable relationships useful in proofs.

Why I enjoy Math

In my opinion, geometry is one of my favorite math topics because it combines logical reasoning with visual problem-solving. Working through segments, angles, and proofs strengthens critical thinking and helps me visualize relationships in space. Solving these problems accurately also improves attention to detail and mathematical rigor, which I find rewarding.