Notes, summaries, assignments, exams, and problems for Secondary education

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" »

Simple Present

Pres. Simp. -> She cleans her.. -> She has her brushes cleaned

Present Continuous

Past Simple

Past Continuous

Future Simple

Future Continuous

Present Perfect

Present Perfect Continuous

Past Perfect

Past Perfect Continuous

The New Man: Humanist Vision

The new man: humanists proposed a new vision of man as the most perfect of God's creations. They considered him the center of universal interest. Freedom and reason: they believed that God had created man as a free being responsible for his actions and capable of rational thought. Scientific interest: in order to expand their knowledge, they used observation and experimentation. Human progress: humanist thought was optimistic. Intellectuals believed in God and the Christian faith. Rediscovery of antiquity: the teachings of classical authors such as Plato and Aristotle were a model for intellectual, social, and political behavior and education.

Demographic and Economic Recovery

In the second half of the 15th century,... Continue reading "The Renaissance: A New Vision of Man and Society" »

Causes of the Protestant Reformation

The 16th century witnessed significant religious conflicts, primarily driven by the Reformation and subsequent Counter-Reformation. Several factors contributed to the widespread desire for change within the Roman Catholic Church.

Disdain for the Papacy and Clergy

The Roman Catholic Church held immense power across Europe. However, many perceived that popes were primarily concerned with their own interests, bishops lived lives of luxury without fulfilling their pastoral duties, and many religious orders failed to adhere to their established rules. This led to a growing disillusionment among the populace.

Abuses Within the Church

Widespread abuses further fueled discontent. These included:

• Nepotism: High-ranking

The Modern Age

A New Historical Period

The Modern Age (15th-18th centuries) is generally considered to have begun with the capture of Constantinople by the Turks in 1453 or with the discovery of America in 1492, and it ended with the French Revolution in 1789.

The Modern Age is divided into several sub-periods:

* 16th century: Renaissance period * 17th century: Baroque period * 18th century: Enlightenment and Absolutism

Changes in the 15th and 16th Centuries

From the mid-15th century to the 16th century, the international landscape underwent significant changes due to these events:

* The disappearance of the Byzantine Empire: Following the capture of Constantinople by the Turks in 1453, Western Christianity felt increasingly under threat from... Continue reading "Modern Age: Transformations, Discoveries, and Key Events" »

Outlet: A store selling goods of a company, usually at a lower price.

Outcome: The result or effect of an action, situation, or event.

Outlook: The likely future situation.

Outing: A short journey made by a group of people.

Onset: A start; a beginning.

Outrage: A strong feeling of shock.

Outbreak: A sudden appearance of a disease.

Outlay: An amount spent at the beginning of a business.

Idioms and Expressions

Break the mould: To be new and different.

Blind someone with science: To confuse somebody by using difficult or technical words.

Move with the times: To change and become more modern because attitudes and fashion are changing.

Be someone's guinea pig: To be the subject of an experiment.

Turn the clock back: To want to return to a past situation because... Continue reading "Essential Vocabulary: Definitions for Modern Concepts" »

Key Industries of the Industrial Revolution

The textile and iron industries were the dominant sectors during this period.

The Textile Industry

In the 18th century, there were large volumes of trade in hand-printed cotton fabric from India (known as indianas). The British government boosted the production of cotton fabric within Britain. The mechanization process started with John Kay's flying shuttle (1733), which increased the speed of production and made it possible to weave wider fabrics. This was followed by spinning machines like the spinning jenny, spinning mule, and water frame, which significantly increased productivity.

The Iron Industry

In the 18th century, there was a huge rise in demand for iron to manufacture ships, munitions, machines,... Continue reading "Key Industries of the Industrial Revolution: Textiles, Iron, and Coal" »

Key 20th-Century Historical Definitions

Stalinism

Stalinism is a totalitarian political system established by Joseph Stalin in the USSR, beginning in 1927.

Totalitarianism

Totalitarianism is a political system where a single party holds total control over the economy and society, establishing an authoritarian state characterized by the rejection of equality, ultra-nationalism, and militarism.

Sovkhozy

Sovkhozy were state-owned farms under Stalin's government where peasants worked for a salary.

Kolkhozy

Kolkhozy were agricultural cooperatives under Stalin's government where land was owned and farmed collectively.

USSR

The USSR (Union of Soviet Socialist Republics) was a political organization created in 1922 by Vladimir Lenin, composed of Russia and other... Continue reading "Key Historical Terms of the 20th Century: Stalinism to WWII" »

The Sense of Hearing and Balance

The sense of hearing is located inside the ears. Sounds are vibrations of the air, received by the eardrum. The eardrum transfers these vibrations to the cochlea, where mechanoreceptors transform them into nerve impulses. These impulses then travel to the brain through the auditory nerve. The sense of balance is also located inside the ear and is closely related to the sense of hearing.

The Organization of the Nervous System

The nervous system is composed of two main divisions: the Central Nervous System (CNS) and the Peripheral Nervous System (PNS).

Central Nervous System (CNS)

• The Central Nervous System (CNS) comprises the brain and the spinal cord. This is where all stimuli are evaluated, and responses are generated.

The Ghost of Coyote Canyon

"Tell me about the old Chumash cemetery and Mr. Richardson," said Nick, as they walked to the barbeque at Blue River Park.

"Oh, you won't believe it, Nick!" said Bill. "People at Coyote Canyon say that on nights when there's a full moon they see an American Indian Warrior. He has a black horse and gallops through the canyon. They think he's a ghost and they're scared!"

"The ghost of an American Indian warrior?" asked Nick, surprised.

"Yeah," said Michelle, "and some people want to sell their new homes!"

"I'm sure Mr. Richardson isn't very happy about that," said Nick.

"No," said Bill, "but he continues building there."

"He and his wife live at Coyote Canyon," said Michelle.

"Have they ever seen the ghost of the warrior?"... Continue reading "The Chumash Cemetery and the Coyote Canyon Legend" »