12 topics of Geometry by Victor Marin

Fundamentals of Geometry

5700481 — 2024-12-09 21:50:12 UTC

Undefined Terms: These are basic concepts that are not formally defined but are understood intuitively. They include:
- Point: A specific location.
- Line: A straight path that extends infinitely in both directions.
- Plane: A flat surface that extends infinitely in all directions.
Distance Formula: Used to calculate the distance between two points on a coordinate plane.
Midpoint Formula: Used to find the midpoint of a line segment.

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B) Conditional Statements and Venn Diagrams

Conditional Statements: Statements that have a hypothesis (if part) and a conclusion (then part).
Venn Diagrams: Visual representations used to show relationships between sets of data.

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Point-Slope Form: A linear equation in the form y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
Standard Form: A linear equation in the form Ax + By = C, where A, B, and C are constants.

5700481 — 2024-12-11 20:49:18 UTC

These are methods to prove that two triangles are congruent (exactly the same shape and size):

SSS (Side-Side-Side): If three sides of one triangle are congruent to three sides of another triangle.
SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.
ASA (Angle-Side-Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle.
HL (Hypotenuse-Leg): For right triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle.

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Quadrilaterals with two pairs of parallel sides.

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Parallelograms with four right angles.

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Parallelograms with four congruent sides.

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Parallelograms with four right angles and four congruent sides.

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Quadrilaterals with exactly one pair of parallel sides.

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A line segment that connects the midpoints of the non-parallel sides of a trapezoid.

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Quadrilaterals with two pairs of adjacent congruent sides.

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