12 Topics of Geometry by Ethan Alfaro Corona

Distance Formula

3403405 — 2024-12-10 15:20:11 UTC

Using given coordinates you plug in the appropriate number to their corresponding letter. For Example if the two pairs of coordinates were (2,1) and (3,4) its would look like, (3-2)^2 + (4-1)^2 = d.

Venn Diagram

3403405 — 2024-12-10 15:23:51 UTC

This type of Venn Diagram is a Disjunction, as some elements of each statement correspond to each other while other elements don't.

Parallel Lines

3403405 — 2024-12-10 15:25:45 UTC

For an example of parallel lines would be Line A and Line B, as they are two coplanar lines that never intersect no matter how long you stretch them out.

Point Slope

3403405 — 2024-12-10 15:36:13 UTC

In the Point-Slope Formula all you need is one pair of coordinates and the Slope (m), you leave the first y unchanged while plugging in your second coordinate in y1's place, repeating this process on the opposite side, and adding one step of inserting (m) Slope, lastly isolating y, and that's your answer.

SSS

3403405 — 2024-12-10 15:40:44 UTC

An SSS Triangle is when all sides are CONGRUENT to each other, for example all sides equaling to 3 would be an SSS triangle.

Parallelograms

3403405 — 2024-12-10 15:44:15 UTC

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel to each other, for example if the sides (A,C) and (B,D) are parallel to each other from Rectangle ABCD, then it is a Parallelogram.

Rectangles

3403405 — 2024-12-10 15:44:38 UTC

For a shape to be classified as a Rectangle, it must have all four CORNER ANGLES equal 90 Degrees.

3403405 — 2024-12-10 15:50:09 UTC

Some classifications for a shape to be classified as a Rhombi are, all four sides must be congruent, Diagonals are perpendicular, and Diagonals Bisect opposite angles.

Squares

3403405 — 2024-12-10 15:55:29 UTC

A square follows all the property rules of parallelograms, rectangles, and rhombuses. Some being, Four Right angles, Diagonals are Congruent, and Four congruent sides.

Isosceles and Non-Isosceles Trapezoids

3403405 — 2024-12-10 16:01:22 UTC

Non-Isosceles Trapezoids - have only ONE pair of Parallel sides, and they should be opposite to each other, and the Consecutive angles between the parallel lines should be supplementary or equal to 180 degrees.
Isosceles Trapezoids - Non-Parallel Sides, Diagonals are congruent, Base Angles are congruent, and Opposite Angles are supplementary.

Midsegment

3403405 — 2024-12-10 16:05:01 UTC

The Mid segment of a trapezoid is (BC+AD) /2 = EF, for example BC equaling 14 and AD equaling 36, the equation would be (14+36) /2 or 50/2, which would be 25,so EF=25.

Kites

3403405 — 2024-12-10 16:07:56 UTC

Kites have two pair of congruent angles or IH=IS and HT=ST, one pair of opposite angles or Angle IHT and Angle IST, and Diagonals are perpendicular or Line IT is perpendicular to Line HS.

Pictures

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Midpoint Formula

3403405 — 2024-12-10 17:06:43 UTC

For midpoint formula you are trying to get the middle of two pairs of coordinates, meaning all you need are two pairs of coordinates, for example (2,4) and (6,8) placed in the equation would be ((2+6)/2, (4+8)/2) or (8/2, 12/2), which after dividing would be (4,6) or the midpoint (m)

Undefined terms

3403405 — 2024-12-10 17:13:51 UTC

There are three undefined terms:

Points - A dot with no dimensions.
Lines - Has 1 dimension, Made up from infinite points, and extends infinitely.
Planes - Has two Dimensions, Represented by a shape that correlates to a floor or wall that extends infinitely, and is named using three non-linear points.

Conditional Statements

3403405 — 2024-12-10 17:31:24 UTC

There are four types of Conditional Statements:

Converse - Is formed by switching the hypothesis and conclusion, q->p
Inverse - Is formed by negating the hypothesis and conclusion, ~p->~q
Contrapositive - Is formed by negating and switching the hypothesis and conclusion, ~q->~p
Biconditional - Is the conjunction of the conditional on its converse,
(p->q) ∧ (q->p) or p ↔ q.

Standard Form

3403405 — 2024-12-10 17:43:22 UTC

Standard form is used when you have an equation in standard form and need the slope or the equation in slope-intercept form, the equation must have x and y on the same side and a number on the other for example, 5x + 2y = -2, you need to isolate the variable y, meaning you must move x, so you would subtract 5x on both sides cancelling it on the left and adding it to right leaving you with 2y = -5x - 2, now you need to remove 2 from 2y, this time dividing 2 from all numbers leaving you with y = -5/2x -2/2, this being your final answer.

Perpendicular Lines

3403405 — 2024-12-10 17:53:58 UTC

Perpendicular Line(s) are :

A straight line that creates 90 degrees when intersecting.
Opposite Reciprocals

Information

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Gina Wilson All Things Algebra (Journal)

SAS

3403405 — 2024-12-10 18:57:31 UTC

An SAS Triangle is when both sides and angles are congruent.

ASA

3403405 — 2024-12-10 18:59:17 UTC

For a triangle to be classifies as "ASA" it must have two angles and the side in between congruent.

AAS

3403405 — 2024-12-11 01:20:56 UTC

For a triangle to be classified as "AAS" it must have two angles and a side opposite to them is congruent.

HL

3403405 — 2024-12-11 01:24:25 UTC

For a triangle to be classified as an "HL" triangle it must have a hypotenuse and any one leg of the right triangle congruent.