Vocabulary Notes

ray – sugár

sets of points – pontok halmaza

subset – részhalmaz

angle – szög

triangle – háromszög

right – derékszögű

acute – hegyesszögű

obtuse – tompaszögű

plane – sík

line segment – szakasz, távolság

vertex (pl.vertices) – csúcs

equilateral – egyenlőoldalú

isosceles – egyenlő szárú

leg – oldal, szár

square – téglalap

quadrilateral – négyszögletes

rectangle – négyszög

intersect v. – átmetsz, kereszteződik

concave – homorú, konkáv

convex – domború, konvex

Exercises

I. Answer the following questions on the text:

1. Do we extend a line segment in two directions when we form a ray?

2. Will two rays originating from the same endpoint form an angle?

3. Do angles separate the plane into 2 distinct sets of points?

4. Is the obtuse angle less than the right angle?

5. Is the right angle greater than the acute angle?

6. Are triangles classified according to the measures of their angles?

7. Can any triangle be referred to as equilateral?

8. Does a right triangle contain three right angles?

9. Are opposite sides of a quadrilateral always parallel?

10. Are all the four angles of a square congruent?

11. Is every rectangle a square?

II. Choose the right name for the following figures. There is one extra name.

a) b) c) d) e) f)

Hexagon, Nonagon (or Enneagon), Octagon, Pentagon, Quadrilateral (or Tetragon), Heptagon (or Septagon), Triacontagon

III. Translate into Hungarian the following geometrical definitions. Learn them by heart.

Geometry treats of the properties, constructions, and measurement of lines, surfaces, and, solids.

A solid has three dimensions, usually designated as length, breadth, and thickness.

A surface has but two dimensions – length and breadth.

A line has but one dimension – length.

A point has no dimension but is simply a position in space.

Parallel lines are lines that are everywhere equally distant from each other.

A horizontal line is a line parallel to the horizon, or water level. The surface of water in a tank is horizontal.

A vertical line is a line straight up and down.

A line is perpendicular to another when it meets or crossesthe other line squarely. Such lines are also said to meet or cross at right angles. A line is also said to be normal to another when it meets the other at right angles.

Angles. – An angle is formed by the meeting or intersection of two straight lines. An angle is measured by the difference in direction of the two lines which form the angle. The point of the angle where the lines meet is called the vertex.

The  sign is often used for the word angle.

A right angle is the angle formed by two lines that are perpendicular to each other. An angle less than a right angle is called an acute angle. An angle greater than a right angle is called an obtuse angle.

Circles and circular measure. – A circle is a flat surface bounded by a curved line all points of which are equidistant from a point within called the centre. The bounding line of a circle is called the circumference.

A straight line drawn from the centre to the circumference is called the radius.

Straight line through the centre, terminating at both ends on the circumference, is called the diameter. The diameter of a circle is equal to twice the radius. The circumference of a circle is equal to 3.1416 times the diameter.

An arc of a circle is any portion of a circumference.

A chord of a circle is a straight line connecting any two points on the circumference.

Circular arcs are measured in degrees, there being 360 degrees in a complete circumference. For finer measurements, degrees are divided into minutes, and minutes into seconds, there being 60 seconds in 1 minute and 60 minutes in 1 degree. Degrees are marked by the sign (°), minutes by ('), and seconds by (˝).

Angular measure. – Angles also are measured in degrees, minutes, and seconds, by swinging an arc of a circle from one side of the angle to the other, using the vertex of the angle as the centre. The number of degrees in the arc gives the number of degrees in the angle. A right angle therefore contains 90°, because two lines at fight angles form four right angles, and these divide a complete circumference of 360° into four equal parts of 90° each. An acute angle has less than 90° while an obtuse angle contains more than 90°.