Notes, summaries, assignments, exams, and problems for Visual arts

A polygon is the portion of the plane bounded by a closed polyline. A polygon is a plane shape with straight sides. A plane is a flat surface with no thickness.
Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is “closed” (all the lines connect up).

1. Circumcenter

The circumcenter is the center of the triangle’s circumcircle, one that passes through the three vertices of the triangle.
It is located at the intersection of the three side bisectors. As we already know the line bisector is the locus of all the circle centers that pass through the endpoints of a segment. As the three sides of a triangle are segments, if we draw the three side bisectors, we will get a point that will be the center of a circle that... Continue reading "Understanding Triangle Centers: Circumcenter, Incenter, Centroid, and Orthocenter" »

Projecting Points and Shapes

Projecting points onto a plane involves rays passing through the points and intersecting the plane. These intersections are called projections. Projecting a shape involves projecting its vertices.

Projection Systems

There are two main systems of projection:

Perspective Projection

When the rays originate from a single point, the system is called perspective projection. The resulting shape is proportionally smaller or larger.

Parallel Projection

When the rays are parallel, the system is called parallel projection. The resulting shape is congruent (same shape and size). There are two variations:

1. Oblique Projection: The rays are oblique to the projection plane.

2. Orthographic Projection: The rays are perpendicular to the projection

Understanding Comics and Cartoons

Cartoons are simple drawings that are often humorous, sometimes satirical, and can be informative. A comic book is a small book or magazine that focuses on pictures to tell a story, rather than just words. If the picture is funny, we are usually talking about a cartoon. If there are multiple pictures with a more realistic style, we are referring to a comic strip or a comic book.

When we have a single image, it is used for recognition and information, like the non-verbal cartoon signs for “walk” and “don’t walk.”

Newspapers frequently feature jokes and stories presented as “comic strips” (a series of drawings).

There is a key difference between cartoon illustration and animated cartoons. Animated cartoons... Continue reading "Understanding Comics and Cartoons: Creation & Design" »

Verb Tenses

Past Simple

Structure: Subject + Verb (past form or -ed) or 3rd column; Negative: didn't + base form.

Uses: Completed actions in the past (with expressions like last, ago, yesterday, in 1992).

Past Continuous

Structure: was/were + verb-ing.

Uses: Actions in progress in the past; Past Continuous + when + Past Simple or Past Continuous + while + Past Continuous.

Past Perfect

Structure: had + past participle (verb-ed or 3rd column).

Uses: An action that happened before another action in the past (with expressions like after, before).

Future Simple (Will)

Structure: will + base form.

Uses: Weather, promises, future predictions, spontaneous decisions.

To Be Going To

Structure: is/am/are + going to + base form.

Uses: Future plans.

Present Simple

Uses:

Essential Travel Vocabulary

Building Vocabulary

• Bathing suit = Traje de baño
• Sandals = Sandalias
• Towel = Toalla
• Tent = Carpa
• Insect repellent = Repelente de insecto
• Sleeping bag = Saco de dormir
• Pair of scissors = Tijeras
• First aid kit
• Brush = Cepillo
• Hair dryer = Secador
• Makeup = Maquillaje
• Shampoo
• Soap = Jabón
• Toothbrush = Cepillo de diente
• Sunscreen = Bloqueador
• Batteries = Baterías
• Razor = Máquina de afeitar
• Flashlight = Linterna

Living Spaces

• Living room: Lamp, end table, cushions, sofa, rug, coffee table, armchair
• Bedroom: Clock, nightstand, curtains, carpet, dresser
• Kitchen: Microwave, stove (cocina), oven (horno), cabinets, faucet (lava plato)
• Bathroom: Mirror, sink (lavamano), toilet, shower, bathtub (tina)

Essential Grammar

Order of Adjectives

Opinion,... Continue reading "Essential Travel Vocabulary and Grammar for Beginners" »

Essential Vocabulary: Clothing and Fashion

• Summer wardrobe
• Finest silk cloth (tela)
• Garment (prenda)
• Their clothes were soaked
• Items of clothing (ropa)
• Sports kit
• Leisure wear
• Evening, formal dress/attire
• New outfit for the party

Style and Design

• Style
• Designer label (etiqueta)
• Classic design
• Brand loyalty
• Bearing their logo
• Recognizable pattern

Adjusting Clothes

• Let out: Make clothes larger
• Take in: Make clothes smaller
• Let down: Make clothes longer
• Take up: Make clothes shorter

Changing Clothes

• Dress up: Wear smart clothes
• Dress down: Wear casual clothes
• Change into: Replace one set of clothes with another
• Change out of: Replace one set of clothes with another
• Wrap up: Put on warm clothes
• Slip on: Put on clothes quickly and easily
• Slip off: Take off clothes quickly and

Essay Writing Structure (140-190 Words)

Essay Structure

1. Introduce the topic briefly and pose a rhetorical question.
2. Develop the main argument (Point 1).
3. Introduce a contrasting viewpoint (e.g., "On the other hand").
4. Conclude with your personal opinion.

Useful Essay Phrases

• Some people claim that...
• It's often said that...
• However, ...
• Firstly, ...
• To clarify the point, ...
• From my point of view, ...
• It seems clear to me that...
• Lastly, ...

Informal Letter Writing (140-190 Words)

Informal Letter Structure

1. Greeting (e.g., Hi [Name]...).
2. Reference the previous email/contact and provide short details.
3. Share your news and respond to their points.
4. Ask interesting questions for the recipient.
5. Discuss when you will meet again.
6. Closing (e.g., All the best, [Your Name]).

Useful

English Grammar Cheat Sheet

Verb Tenses

Present Simple

Actions that happen habitually. Subject + Verb (e.g., I don't talk, he eats)

Present Continuous

Action happening at this moment: Subject + to be + gerund (e.g., I'm talking, he isn't eating)

Past Simple

Action that began and ended in the past: Subject + past tense verb (e.g., She was/wasn't a doctor, I wanted/didn't want to dance)

Past Continuous

Action interrupted in the past (e.g., I was talking)

Present Perfect Simple

e.g., I have talked to Peter / He hablado con Peter

Past Perfect Simple

e.g., They had studied (habían estudiado)

Future Simple

Predicting the future: I will call you tonight / be going to (planned future action) - I'm going to call you.

Future Perfect Simple

Actions completed by a certain... Continue reading "English Grammar Cheat Sheet: Tenses, Reported Speech, and More" »

Present Continuous

Actions that are happening now.

• Add -ing to the verb (e.g., I am talking, he/she/it is eating, you/we/they are talking).

Present Simple

Actions that happen regularly or habitually.

• For I, you, we, and they, use the base form of the verb (e.g., talk, eats, learn).
• For he, she, and it, add -s to the verb (e.g., talks, eats, learns).
• For questions, use do/does and do not add -s (e.g., Do you talk?, Does he eat?).
• For negatives, do not add -s (e.g., I don't talk, he doesn't learn).
• Use time expressions (e.g., always, usually, often, sometimes) before the verb.

Present Perfect

Past actions that have relevance to the present.

• For I, you, we, and they, add have.
• For he, she, and it, add has.
• Affirmative: I have (I've) talked to Peter, they have