Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles are usually presumed to be in a Euclidean plane, but are also defined in non-Euclidean geometry. Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of an angle (figure), the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. The word angle comes from the Latin word angulus, meaning "a corner". The word angulus is a diminutive, of which the primitive form, angus, does not occur in Latin.Cognate words are the Greek , meaning "crooked, curved," and the English word "ankle". Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow". Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; the second byCarpus of Antioch, who regarded it as the interval them to annnihlate the angles.
...■■ Types of angles
Acute (0–90°) Right (90°) Obtuse (90–180°)
Straight (180°) Reflex (180–360°) Revolution (360°)
■■ Special pairs of angles at a point include:
• Complementary angles (sum to 90°) a + b = 90
• Supplementary angles (sum to 180°) a + d = 180
• Vertically opposite angles (equal) a = c
■■ Angles in a revolution sum to 360°.
■■ Two lines are perpendicular if they intersect at
right angles (90°).
■■ 8 point compass bearing
• Bearings are usually measured clockwise
from north.
■■ A transversal is a line cutting at least two other lines.
■■ Pairs of anglesformed by transversals can be:
• corresponding (in corresponding positions)
• alternate (on opposite sides of the transversal and
inside the other two lines)
• Co-interior (on the same side of the transversal and inside
the other two lines).
■■ Lines are parallel if they do not intersect.
• Parallel lines are marked with the same number of arrows.
or
■■ If two parallel lines are cut by a transversal
• the corresponding angles are equal (4 pairs)
• the alternate angles are equal (2 pairs)
• the co-interior angles are supplementary
(sum to 180°) (2 pairs).
A triangle with vertices A, B and C is written Δ ABC.
■■ The minimal conditions for a unique triangle are:
• SSS (3 sides)
•...
...Korah Agre
January 26, 2011
EN130-3
TwoAngles of Vision
Part A: Positive Description
As I sit here staring at these whites walls, I find it very easy to ponder with my artistic thoughts. They look as though they are waiting to be filled with memories and creative ideas. The strangely arranged area shows the unique, fun, and creative personalities of the beings that live in this enclosed room; it’s almost as if a burst of happiness blew up in here the night before today. Ryan Sheckler, taking up one large portion of the wall is extremely inviting and dreamy to look at, I gaze into his eyes every time I look up and ponder.
The sweet discussions between best friends make me feel like we are a close family that will always be there through the thick and the thin. I hear the continuous jams playing out of a laptop; it’s comforting like I’m sitting at a poolside enjoying the evening’s sunset. The TV’s resonance sings as if two young teenagers have fallen in love first the first time. Wrapping it all together I hear a humming from the bathroom that as if I was sitting on my grandma’s porch, sipping ice tea, reminiscing about back in the good old days.
The delightful scent of meadows and rain feels like I’m resting in a cool, green jungle. As I run my fingers over the smooth touch of the keys, I feel as though my fingertips are ice-skating across a just worked ice arena. A sweet taste loiters my mouth as I continue chewing...
...To teach students what an angle is, what types of angles there are, how to measure an angle, and lastly, how to properly read any given angle.
Materials needed for project:
Cut two pieces of card board, or something else that has the same stiff quality as cardboard, into two rectangles
A nut and bolt,
Plastic protractor
Activity: Putting together the two cardboard (or other pieces) together to make two hinged pieces.
What happens next:
As you can see in the photograph one arm is attached to the other with the nut and bolt.
When the arms are fixed together it can be explained about the angle that is formed between the arms. It needs to be explained as well that the angle increases when moved clockwise and that it decreases when moved counter clockwise.
Here is where the protractor comes in handy: The protractor is half of a circle which is 360, so the protractor is 180 degrees. It can be used to easily measure the degree of the angles.
Explain the differences in all degrees and their names:
Use the item you made to show an angle that is less than 90 degrees, which would be called an acute angle.
When the measure of the angle is 90 degrees, it is called a right angle.
When the measure is between 90 and 180 degrees,...
...Morehouse College in 1944 and then went to Crozer Religious Seminary to undertake postgraduate study, receiving his doctorate in 1955.
Returning to the South to become pastor of a Baptist Church in Montgomery, Alabama, King first achieved national renown when he helped mobilise the black boycott of the Montgomery bus system in 1955. This was organised after Rosa Parks, a black woman, refused to give up her seat on the bus to a white man - in the segregated south, black people could only sit at the back of the bus. The 382-day boycott led the bus company to change its regulations, and the supreme court declared such segregation unconstitutional.
In 1957, King was active in the organisation of the Southern Leadership Christian Conference (SCLC), formed to co-ordinate protests against discrimination. He advocated non-violent direct action based on the methods of Gandhi, who led protests against British rule in India culminating in India's independence in 1947.
In 1963, King led mass protests against discriminatory practices in Birmingham, Alabama where the white population were violently resisting desegregation. The city was dubbed 'Bombingham' as attacks against civil rights protesters increased, and King was arrested and jailed for his part in the protests.
After his release, King participated in the enormous civil rights march on Washington in August 1963, and delivered his famous 'I have a dream' speech, predicting a day when the promise of freedom and...
...Angle of Incidence vs. Angle of Reflection
October 23, 2011 by alison12 · No Comments · Uncategorized
Angle of Incidence vs. Angle of Reflection
Background Information:
Reflection is the change of direction of light. The angle a light ray makes is the same after reflection occurs as it is before reflection occurs. Reflection is the image seen when looking into a mirror, still water, or a polished surface. The reflected image seen will be the same as the object which is being reflected.
Aim:
To investigate what the relationship is between the angle of incidence and the angle of reflection.
Hypothesis:
The angle of reflection will equal the angle of incidence.
Materials:
One mirror
One power supply
One light box kit
One protractor
One A4 sheet of paper
Safety:
The light box could become hot, so be careful not to touch it.
Do not stick anything inside the power supply.
Safety goggles, lab coats and other safety equipment are not required for this experiment.
Variables:
Independent Variable: Angle of incidence
Dependent Variable: Angle of reflection
Controlled Variable: Mirror
Method:
1. Draw on the A4 sheet of paper the normal.
2. Set up all equipment such that the light reflects off the mirror as shown in the diagram below:
Science Focus 4
1. Make the angle of...
...____________________________________ Score:______________
Section: __________________ Date:_______________
Activity No. 1.1
Unit of Measurement
I. Convert each angle to a decimal in degrees.
1. 40° 30' 2. 60° 60' 60"
II. Convert each angle to D° M' S" form.
1. 40.3° 2. 118.255°
III. Evaluate the following.
1. Complement of 74° 31' 43"
2. Supplement of 105° 24' 56"
Activity No. 1.2
Unit of Measurement
I. Convert each angle in degrees to radians.
1. 67.5°
2. –300°
II. Convert each angle in radians to degrees.
1.
2.
Activity No. 1.3
Angles in Standard Position/Co-terminal Angles
I. Draw each of the following angles in standard position.
1.
2.
II. Solve for the following.
1. Find the twoangles (one positive and one negative) that are co-terminal with -75°.
2. Find an angle between 0° and 360° that is co-terminal with 1110°π3.
III. Given are the measures of twoangles in standard...
...STUDENT REPORT
27 August 2012
Duration 40 mins | Examcode 6169451
Multiples and Lines and Angles
Factors;
SCHOOL
Children^s Academy, Malad
CLASS 5
DIVISION D
STUDENT
VORA CHAITYA NIRAV
ROLL NO 25
YOUR PERFORMANCE IN THE TEST: 81.82% The class average performance in this topic is 68.8% BEST PERFORMANCE IS IN SUBTOPIC Understanding of factors and multiples TWO SUB TOPICS RECOMMENDED FOR IMPROVEMENT * Understanding of lines * Understanding of angles.
1
DA STUDENT REPORT
CLASS 5 ROLL NO 25
Multiples and Factors; Lines and Angles
DATE 27 August 2012
Misconceptions Concept: Application of HCF in Real Life
10
Q Reema has 3 pieces of ribbon which are 18 m, 36 m and 45 m long respectively. She wants to cut them into pieces of equal length. She wants to do this in such a way that no ribbon is wasted. What is the length of the LONGEST piece that she can get? 1 3m 2 6m 3 9m 4 15 m
Correct Option: 3
Student Selection: 1
Students who have answered A seem to have realised that the required length should be a common factor of 18, 36 and 45. But they seem to have opted for the common factor that is clearly visible, and have not thought beyond the obvious. It is also possible that they have not noticed the word longest in the question, or may not have realised that they have to find the HCF here. Students answering incorrectly are unable to apply their understanding of...
...Final Essay
Pd.4
War can change a person’s perspective and gain one’s maturity. Not only let a person to be more considerate for others, but also increase a person’s courage. Throughout the Fallen Angels, the war changes the soldiers a lot. For example, the innocent young soldiers enter the war, it quickly changes them and forces them to develop into men. The relationship between the squad members have also changed and make their friendship even more strongly bonded. In addition, Perry’s point of view for the war has also changed.
In the beginning, Perry didn’t really think about joining the army. The reason he goes to Vietnam because he wants to earn money for his brother Kenney. The captain said, ‘’ The only reason you’re going to Nam is that it takes forever to process a medical profile. Once it catches up with you, you’ll be headed home’’(Myers 5). Perry wasn’t that worry about the war because he expect that his medical profile will be processed correctly and he won’t have to go into combat. He also believes that peace is not far off and most of the soldiers don’t actually have to fire their guns. Before joining the army, Perry didn’t realize the romantic, idealized concept of war and the harsh reality of it. And other soldiers in the squad also have less clear idea of what war is really like. After Perry arrives to Vietnam, he begins to see that the war is characterized by fear, rather than heroic. Perry said to Peewee, ‘’ ‘His weapon didn’t work. If it had,...
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