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Geometry.Campo-2#
General Definitions (Also definitions for proofs)
| Term | Definition |
|---|---|
| Partitioning | Separate or divide into smaller pieces. |
| Inductive reasoning | A type of reasoning that reaches conclusions based on patterns of specific examples or pat events. This reasoning is where we make predictions based on patterns, not facts. (Flawed) |
| Deductive reasoning | A process of reasoning using given and previously known facts to reach a logical conclusion. |
| Adjacent | Angles that are Coplanar that have a common side and and a common vertex, but no interior points. |
| Linear | Adjacent angles whose non shared rays form opposite rays. |
| Supplementary | Angles that that come to a sum of 180 degrees. |
| Complementary | Angles that come to a sum of 90 degrees. |
| Vertical | Two angles that have sides that form two pairs of opposite rays. |
| Theorem | A conjecture (a set of lining things up, like a pattern) that is proven true. |
| Proof | A convincing mathematical argument that uses deductive reasoning to prove conditional statements true. (It shows how we get from the given hypothesis to our conclusion with mathematical justifications.) |
| Definition of Congruence | m∠A = m∠B <-> m∠B = m∠A (Angles are equal) |
| Definition of angle bisector | An angle bisector divides (Chops in half) an angle into two equal parts. |
| Definition of perpendicular | Perpendicular lines form right angles. |
| Definition of a right angle | A right angle = 90 degrees. |
| Definition of Midpoint | The midpoint of a segment divides the segment into two equal (congruent) parts. EX: If M is the midpoint of line AB, then AM=MB |
| (Unit 2) Transversal | A line that intersects two or more lines Traversals can intersect either parallel or non-parallel lines |
| (Unit 5) Altitude | A perpendicular segment from a vertex of a triangle to the line containing the opposite side or opposites vertex. |
| Median | A segment that has endpoints at a vertex and the midpoint of the side opposite the vertex. |
| Concurrent Lines | Three or more lines that intersect at the same point |
| Point of Concurrency | A point where three or more lines intersect. |
| Point of Concurrency of Medians | The Medians of a triangle are concurrent at a point that is 2/3 the distance from each vertex to the midpoint of the opposite side. (AKA "The centroid measure theorem".) |
| Centroid | The point of concurrency of medians. Also known as... Balancing point of triangles, Center of gravity, (The bigger part of the median is always double the shorter part.) |
| Concurrency of Altitudes | The lines that contain the altitudes of a triangle are concurrent |
| Orthocenter | The point of concurrency for altitude of a triangle. Can fall in three possible places: in, on, or outside of a triangle. |
| Where does the orthocenter fall? Acute triangle:... | Inside. |
| Where does the orthocenter fall? Right triangle:... | On. (Always on the right angle) |
| Where does the orthocenter fall? Obtuse triangle:... | Outside. |
| A circle is _______________ about a polygon if the vertices of the polygon are on the circle. | Circumscribed |
| A circle is ______________ in a polygon if the sides of the polygon are tangent to the circle. | Inscribed |
| What is equidistant from its vertices? | The circumcenter |
| What is equidistant from its sides? | The Incenter |
Created by:
PaigeRyals-9th
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