Geometry by Isaac Perez

Foundations of Geometry

2702106_1 — 2024-12-09 21:43:05 UTC

Point- its represented by a dot and has no dimensions

EX: A.

Line- has one dimension, made up from infinitely points, and extends indefinitely in two directions

EX: Line AB

Plane- has two dimensions, represented by shape, but a plane extends indefinitely far.

EX: Plane P or Plane ABC

Distance formula- d = √(x₂ - x₁)² + (y₂ - y₁)²

Mid point formula- (xM,yM)=x1+x22,y1+y22)

Conditional Statements and Venn Diagrams

2702106_1 — 2024-12-10 03:27:00 UTC

Conditional Statements- are statements that can be written if-them form. The hypothesis is the phrase that immediately follows if. The conclusion is the phrase that immediately follows them.

EX: If you live in Nashville, then you live in Tennessee. Hypothesis: you live in Nashville. Conclusion: you live in Tennessee.

Venn Diagram- there are types of venn diagram, All, Some, and No. All elements of p are elements of q. Some elements of p are elements of q. There is No relationship between p and q.

EX: All: p -> q, Some: p v q or p ^ q

Parallel and perpendicular lines

2702106_1 — 2024-12-10 04:12:18 UTC

Parallel lines- two coplanar lines that never intersect

EX: train tracks because they run side by side.

Perpendicular lines- two lines that cross each other and make a right angle.

EX: a cross because it makes 4 right angles.

Point-slope and Standard form

2702106_1 — 2024-12-10 04:31:43 UTC

Point-slope- When given a point (x1, x2) through which the line passes and the slope of the line (m), we can write the equation in point-slope form

EX: y-y₁=m(x-x₁)

Standard form- Because standard form doesn't give you slope (m), you must be able to convert them to slope-intercept form.

EX: Ax+By=C

Triangle Congruence: SSS, SAS, ASA, AAS, HL

2702106_1 — 2024-12-10 05:23:02 UTC

SSS- three pairs of congruent sides

SAS- two sides and an included angle are congruent

ASA- two angles and an included sides are congruent

AAS- two angles and a side opposite them are congruent

HL- the hypotenuse and any one leg of a right angle

Parallelograms

2702106_1 — 2024-12-10 05:30:41 UTC

Parallelograms- a quadrilateral in which both pairs of opposite sides are parallel. They have opposite sides that are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other.

Rectangles

2702106_1 — 2024-12-10 05:44:57 UTC

Rectangles- opposites sides are congruent. Opposite sides are parallel. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisects each other. All 4 corners are 90 degrees. Diagonals are congruent.

Rhombi

2702106_1 — 2024-12-10 05:52:59 UTC

Rhombi- opposite sides are congruent. Opposite sides are parallel. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. 4 sides are congruent. Diagonals are perpendicular. Diagonals bisects opposite angles.

Squares

2702106_1 — 2024-12-10 06:02:28 UTC

Squares- opposite sides are congruent. Opposite sides are parallel. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisects each other. Four right angles. Diagonals are congruent. Four congruent sides. Diagonals are perpendicular. Diagonals bisect opposite angles.

Trapezoids

2702106_1 — 2024-12-10 16:07:40 UTC

Trapezoids- There are two types of trapezoids, non-isosceles and isosceles.

Non-isosceles- only one pair of opposite sides are parallel. Consecutive angles between parallel lines are supplementary.

Isosceles- non-parallel sides (legs) are congruent. Diagonals are congruent. Base angles are congruent. Opposite angles are supplementary.

Midsegment of a trapezoid

2702106_1 — 2024-12-10 16:11:30 UTC

Midsegment of a trapezoid- The midpoint of a trapezoid connect the midpoint of the legs. If segment PQ is the midsegment of trapezoid ABCD, then AB, CD, and PQ are all parallel. To find PQ you would multiply PQ by 2 and that would equal to AB + DC.