Bài tập tiếng anh nghiên cứu hình sơ cấp

Bài tập tiếng anh nghiên cứu hình sơ cấp

Bài tập tiếng anh: nghiên cứu hình sơ cấp. Sinh viên thực hiện: Giáo viên hướng dẫn: Trần Đình Tuấn (nhóm trưởng) Tiến sĩ: Đào Thị Huyền Thương. Phạm Nguyễn Thu Trang Nguyễn Huyền Trang. Nguyễn Thị Hải Yến. Nguyễn Ngọc Thúy. Phạm Mai Trang. Chapter I Lines, Angles, and Triangles Vocabulary: Derive: nhận được từ,lấy được từ, suy ra. Establish: thiết lập. Survey: điều tra. Navigation: đạo hàng, môn dẫn đường. Astronomy: thiên văn học. Occupations: sự chiếm, sự gữi. Systematize: hệ thống hóa. Undefined: không xác định. Underlie: nằm ở dưới. Description: sự diễn tả, mô tả. Position: vị trí. Chalk: phấn, đá phấn. Civilization: nền văn minh. Equidistant: cách đều. Circumference: dường tròn, chu vi đường tròn. Interchangeable: đổi lẫn được, hoán vị được. Magnitude: độ lớn độ dài, chiều đo. Altitude: chiều cao độ cao. CONGRUENT: đồng dư. 2 1.1 HISTORICAL BACKGROUND OF GEOMETRY The word geometry is derived from the Greek words geos (meaning earth) and metron (meaning measure). The ancient Egyptians, Chinese, Babylonians, Romans, and Greeks used geometry for surveying, navigation, astronomy, and other practical occupations. The Greeks sought to systematize the geometric facts they knew by establishing logical reasons for them and relationships among them. The work of such men as Thales F00 B.C.), Pythagoras E40 b.c), Plato C90 b.c), and Aristotle C50 B.C.) in systematizing geometric facts and principles culminated in the geometry text Elements, written about 325 B.C. by Euclid. This most remarkable text has been in use for over 2000 years. 1.2 UNDEFINED TERMS OF GEOMETRY: POINT, LINE, AND PLANE 1.2.1 Point, Line, and Plane Are Undefined Terms These undefined terms underlie the definitions of all geometric terms. They can be given meanings by way of descriptions. However, these descriptions, which follow, are not to be thought of as definitions. 1.2.2 Point A point has position only. It has no length, width, or thickness. A point is represented by a dot. Keep in mind, however, that the dot represents a point but is not a point, just as a dot on a map may represent a locality but is not the locality. A dot, unlike a point, has size. 3 1.2.3 Line A line has length but has no width or thickness. A line may be represented by the path of a piece of chalk on the blackboard or by a stretched rubber band. Two lines intersect in a point A straight line is unlimited in extent. It may be extended in either direction indefinitely. A ray is part of a line. It has one end point and extends to infinity in one direction. A ray is named starting with its end point first and then any other point on the ray second. 1.2.4 Planes A plane has length and width but no thickness. It may be represented by a blackboard or a side of a box; remember, however, that these are representations of a plane but are not planes. In mathematics, a plane is any flat, two-dimensional surface. A plane is the two dimensional analogue of a point (zero-dimensions), a line (one-dimension) and a space (three-dimensions). Planes can arise as subspaces of some higher dimensional space, as with the walls of a room, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry. A plane surface (or plane) is a surface such that a straight line connecting any two of its points lies entirely in it. A plane is a flat surface. 1.3 LINE SEGMENTS In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. 4 Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment is either an edge (of that polygon) if they are adjacent vertices, or otherwise a diagonal. When the end points both lie on a curve such as a circle, a line segment is called a chord (of that curve). 1.4 CIRCLE 1.4.1 History “The circle has been known since before the beginning of recorded history. It is the basis for the wheel, which, with related inventions such as gears, makes much of modern civilization possible. In mathematics, the study of the circle has helped inspire the development of geometry and calculus. Early science, particularly geometry and astrology and astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles”. 1.4.2 Definition A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the centre (or center; cf. American and British English spelling differences). The common distance of the points of a circle from its centre is called its radius. Circles are simple closed curves which divide the plane into two regions, an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure (also known as the perimeter) or to the whole figure including its interior. However, in strict technical usage, "circle" refers to the perimeter 5 while the interior of the circle is called a disk. The circumference of a circle is the perimeter of the circle (especially when referring to its length). A circle is a special ellipse in which the two foci are coincident. Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone. 1.4.3 Diameter The diameter of a circle is the length of a line segment whose endpoints lie on the circle and which passes through the centre of the circle. This is the largest distance between any two points on the circle. The diameter of a circle is twice its radius. As well as referring to lengths, the terms "radius" and "diameter" can also refer to actual line segments (respectively, a line segment from the centre of a circle to its perimeter, and a line segment between two points on the perimeter passing through the centre). In this sense, the midpoint of a diameter is the centre and so it is composed of two radii. 1.4.4 Chord A chord of a circle is a line segment whose two endpoints lie on the circle. The diameter, passing through the circle's centre, is the longest chord in a circle. A tangent to a circle is a straight line that touches the circle at a single point. A secant is an extended chord: a straight line cutting the circle at two points. 1.4.5 Arc An arc of a circle is any connected part of the circle's circumference. A sector is a region bounded by two radii and an arc lying between the radii, and a segment is a region bounded by a chord and an arc lying between the chord's endpoints. 6 1.5 ANGLES 1.5.1 An Angle in Geometry In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other (see "Measuring angles", below). Where there is no possibility of confusion, the term "angle" is used interchangeably for both the geometric configuration itself and for its angular magnitude (which is simply a numerical quantity). 1.5.2 A Right Angle A right angle is an angle with measure equal to 90 degrees. 1.5.3 An Acute Angle An acute angle is an angle with a measure between 0 and 90 degrees. 7 1.5.4 An Obtuse Angle An obtuse angle is an angle with a measure between 90 and 180 degrees. 1.5.5 Complementary Angles Two angles are complementary if the sum of their measures is equal to 90 degrees. Example: angles a and b with measures a = 19 o and b = 71 o are complementary since a + b = 90 o 8 1.5.6 Supplementary Angles Two angles are supplementary if the sum of their measures is equal to 180 degrees. Example: angles a and b with measures a = 122.1 o and b = 57.9 o are supplementary since a+b = 180 o . 1.6 TRIANGLES 1.6.1 Definition A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ABC. In Euclidean geometry any three non-collinear points determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space). 1.6.2 Classifying Triangles Triangles are classified according to the equality of the lengths of their sides or according to the kind of angles they have. Triangles According to the Equality of the Lengths of their Sides. 9 1.6.2.1. Scalene triangle: A scalene triangle is a triangle having no congruent sides. 1.6.2.2. Isosceles triangle: An isosceles triangle is a triangle having at least two congruent sides. 1.6.2.3. Equilateral triangle: An equilateral triangle is a triangle having three congruent sides. Scalen Triangle *no sides are equal *all angles are different Isosceles Triangle *two sides are equal *angles opposite the equal sides are equal Equilateral Triangle *all sides are equal and all angles are equal to 60 0 1.6.3 Triangles According to the Kind of Angles 1.6.3.1.Right triangle: A right triangle is a triangle having a right angle. 1.6.3.2. Obtuse triangle: An obtuse triangle is a triangle having an obtuse angle. 1.6.3.3. Acute triangle: An acute triangle is a triangle having three acute angles. 10 [...]... sides, then S = (n -2)1800 + The sum of the measures of the extreior angles of any polygon equals 3600 18 Chapter 4 Parallelagrams,Trapezoids,Medians, and Midpoints 4.1:vocabuary Trapezoids: hình thang Parallelagrams: hình bình hành Median: đường trung bình Parallelgrams: các cạnh song song Midpoint:trung diểm A base:cạnh đáy A leg: cạnh bên 4.2: Definion and properties: 4.2.1 Trapezoids: - Trapezoid is... triangles : Lượng giác có nghĩa là "đo lường của tam giác." Hãy xem xét các bộ phận của nó: tri có nghĩa là "ba," gon có nghĩa là "góc", và metry có nghĩa là "thước đo." Như vậy, trong lượng giác chúng tôi nghiên cứu đo lường của tam giác The following ratios relate the sides and acute angles of a right triangle: 1.Tangent ratio: The tangent (abbreviated "tan") of an acute angle equals the length of the leg . Bài tập tiếng anh: nghiên cứu hình sơ cấp. Sinh viên thực hiện: Giáo viên hướng dẫn: Trần Đình Tuấn (nhóm trưởng) Tiến. 18 Chapter 4 Parallelagrams,Trapezoids,Medians, and Midpoints 4.1:vocabuary Trapezoids: hình thang Parallelagrams: hình bình hành Median: đường trung bình Parallelgrams: các cạnh song song Midpoint:trung