PLANE GEOMETRY-2D SHAPES If you need help, visit www.mathsisfun.com You will find the vocabulary of this unit on pages 6-8
1.- What is a polygon?
2.- When is it regular?
3.- Define Perimeter of a polygon:
4.- Define: a) circle
5.- Translate the name of the elements drawn in the following circumference:
Cuerda: Arco: DiĂĄmetro: Semicircunferencia: Centro: Radio: 6.- Explain how can we get ď ° from a circumference.
7.- Find the length of a circumference of 2 cm of radius.
8.- Write, in English, the names of the types of triangles that you can see below: a) In relation to the angle that is inside:
b) In relation to its sides:
9.- What is a quadrilateral?
10.- Write the first 20 decimal places of ď ° .
11.- Write the statement of the Pythagorean Theorem.
12.- Calculate the hypotenuse of a right-angled triangle whose catheti measure 15 and 8 cm.
13.- Calculate the diagonal of a rectangle with 16m of length and 12 m of width.
14.- A square has 3 600 m2 of surface. What is the measurement of every one of its sides?
15.- a) How many degrees measures every one of the angles in an isosceles right triangle?
b) How many degrees measure every one of the angles in an equilateral triangle?
16.- The perimeter of an isosceles triangle is 23 cm. If the base measures 5 cm, what are the measurements of the other sides?
17.- Draw the plane of the floor of your bedroom and calculate its area. To do it, youâ€™ll have to divide the figure into other known figures such as trianglesâ€Ś
18.- Complete the following table; use the following letters: base: b - height: h - major diagonal: D - minor diagonal: d - side: L - bigger base: B - shorter base: b - radius: r
Formula of the area 2D-sape
Polígono Figura plana Cuadrilátero Área Polígono regular Radio Diagonal Apotema
= = = = = = = =
polygon 2-D shape quadrilateral area regular polygon radius diagonal apothem
Triángulo Triángulo equilátero Triángulo isósceles Triángulo escaleno Triángulo rectángulo Triángulo acutángulo Triángulo obtusángulo
= = = = = = =
triangle equilateral triangle isosceles triangle scalene triangle right-angled triangle acute triangle obtuse triangle
Ángulo recto Ángulo agudo Ángulo obtuso Ángulos complementarios Ángulos suplementarios
= right angle = acute angle = obtuse angle = complementary angles: their measures add up to 90 degrees = supplementary angles: their measures add up to 180 degrees
Linea recta Semirrecta Segmento Rectas paralelas Rectas perpendiculares
= = = = =
straight line ray segment parallel lines perpendicular lines
Circunferencia Diámetro Cuerda Arco Centro (de la circunf.) Círculo Semicírculo
= = = = = = =
circumference diameter chord arc central point circle semicircle
Figuras circulares Sector circular Corona circular
= circular shapes = circular sector = circular crown
Paralelogramo Trapecio Trapezoide Rectángulo Cuadrado Rombo
= parallelogram = trapecium (UK) --- trapezoid (US) = --- trapecium (US) = rectangle
Octógono Eneágono Decágono
Fórmula Base Altura de un triángulo
Diagonal mayor Diagonal menor Base mayor
= major diagonal
= shorter base
Lado Vértice Eje
Punto medio Longitud Longitud del lado
= middle point
= cathetus (pl. catheti) or leg
= square = rhombus
= nonagon = decagon
= base = height/altitude of a triangle
= minor diagonal = bigger base
= corner or vertex (pl. vertices) = axis = length = side-length
Teorema de PitĂĄgoras
Altura de un triĂĄngulo
= Pythagorean Theorem: The sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse. = height or altitude of a triangle: An altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side. The three altitudes intersect in a single point, called the orthocenter of the triangle.
= perpendicular bisector: A line which cuts another line into two equal parts at 90Â°. The three perpendicular bisectors meet in a single point, the circumcenter.
= angle bisector: The bisector of an angle is the line that divides the angle into two equal parts. The intersection of the angle bisectors is the incenter.
= median: A median of a triangle is a straight line through a vertex and the midpoint of the opposite side. The intersection of the medians is the centroid.
Circumference: A line which forms a closed loop. Every point on the line is a fixed (exact distance) from a central point. Radius (radii pl.): A straight line from the centre to a point on the circumference. Diameter: A straight line going from a point on the circumference through the centre to the opposite point on the circumference. A diameter is twice the length of a radius. Chord: A straight line going from a point on the circumference to another and which does not pass through the centre. Arc: A portion of the circumference. Circular sector: The area enclosed by two radii of a circle, and the enclosed arc. Circular segment: The region between a chord of a circle and its associated arc. Page 8