3ºESO- BASIC GEOMETRIC CONSTRUCTIONS

BASIC GEOMETRIC CONSTRUCTIONS

Geometry

Geometry is a kind of mathematics that deals with shapes and figures. Geometry explains how to build or draw shapes, measure them, and compare them. People use geometry in many kinds of work, from building houses and bridges to planning space travel.

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SET SQUARE INTRODUCTION 30/60/90 &45 DEGREES

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SET SQUARES.

SET SQUARES (tools) a thin flat piece of plastic, metal, etc, in the shape of a right-angled triangle, used in technical drawing.

RIGHT ISOSCELES TRIANGLE

RIGHT SCALENE TRIANGLE

SET SQUARES.

SET SQUARES are used to draw angles of 90º, 45º, 30º, 60º or a combination of these angles.

RIGHT ISOSCELES TRIANGLE

RIGHT SCALENE TRIANGLE

Drawing parallel and perpendicular lines.

PARALLEL LINES Look at where the 45º and 60º/30º set squares are positioned in the picture on the left. This position enables us to draw parallel lines. The 60º/30º set square stays in the same place, whilst the 45º set square slides down the page to draw lines at different horizontal positions. These lines are therefore parallel.

Drawing parallel and perpendicular lines.

PERPENDICULAR LINES To draw perpendicular lines, you simply have to rotate the 45º set square, as shown in the picture on the right. Meanwhile, the 60º/30º set square stays in its original position. When you move the 45º set square, you can draw lines that are parallel to one another and perpendicular to the original lines.

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HOW TO DRAW PARALLEL AND PERPENDICULAR LINES USING SET SQUARES.

Construction of angle- Using Set Squares

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CONSTRUCTION OF ANGLE-USING SET SQUARES

SET SQUARES.

BASIC GEOMETRIC CONSTRUCTIONS

LINE SEGMENT - Copy a line segment - Add line segments - Substract line segments - Line segment bisector and right angle.

CIRCUMFERENCE, CIRCLE AND ARC

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ANGLES - Same (congruent angle) -Add angles -Substract angles - Angle bisector

THALES THEOREM -Cut a line segment into n equal segments.

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LINE SEGMENT

The part of a line that connects two points.It is the shortest distance between the two points.

LINE SEGMENT

SECTION

• COPY A LINE SEGMENT

• ADD LINE SEGMENTS.

• SUBSTRACT LINE SEGMENTS.

• LINE SEGMENT BISECTOR AND RIGHT ANGLES.

• SAME (CONGRUENT ANGLE)

• ADD ANGLES

• SUBSTRACT ANGLES

• ANGLE BISECTOR

ANGLES

• Acute Angle is less than 90°
• Right Angle is 90° exactly
• Obtuse Angle is greater than 90° but less than 180°
• Straight Angle is 180° exactly
• Reflex Angle is greater than 180°
• Full Rotation is 360° exactly3

ANGLES

ACTIVITY: ANGLES: ACUTE, OBTUSE...

ANGLES

ACTIVITY

ANGLES

Complete the table by filling in the size of each angle described.

ACTIVITY

ANGLES. Using the protractor

ANGLES. How to use a protractor to measure an angle.

ANGLES. How to use a protractor to measure an angle.

ANGLES. How to use a protractor to measure an angle.

ANGLES. How to use a protractor to measure an angle.

COMPLEMENTARY ANGLES

QUIZ

SUPLEMENTARY ANGLES

QUIZ

ACTIVITY CLOCKS AND ANGLES

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What is the angle between the hands of a clock at 1 o'clock?

¿Qué ángulo forman las manillas de un reloj a la una?

ACTIVITY CLOCKS AND ANGLES

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What is the angle between the hands of a clock at 1 o'clock?

360° ÷ 12 = 30° So the angle between the hands of a clock at 1 o'clock is 30° .

360° ÷ 12 = 30°, por tanto, el ángulo entre las manillas del reloj a la una es de 30° .

ACTIVITY CLOCKS AND ANGLES

SECTION

What is the angle between the hands of a clock at 2:30?

Cuál es el ángulo entre las manillas de un reloj a las 2:30?

ACTIVITY CLOCKS AND ANGLES

• The angle between the 5 and the 6 is 30°
• The angle between the 4 and the 5 is 30°
• The angle between the 3 and the 4 is 30°
• The remaining angle is ½ × 30° = 15°

So the angle between the hands of a clock at 2:30 = 30° + 30° + 30° + 15° = 105°

SECTION

What is the angle between the hands of a clock at 2:30?

• El ángulo entre las 5 y las 6 es de 30º
• El ángulo entre las 4 y las 5 es de 30º
• El ángulo entre las 3 y las 4 es de 30º
• El ángulo restante es la mitad de 30º (15º)
• Por tanto, el ángulo entre las manillas del reloj a las 2:30 = 30º+30º+30º+15º=105º

CIRCUMFERENCE CIRCLE

CIRCUMFERENCE CIRCLE

CIRCLE is the name of a two-dimensional shape and a one-dimensional curve.CIRCUMFERENCE is the perimeter of the circle. In other words it is the length of the boundary of circle. The shape has a certain property that any point lying on the shape is always at a constant distance from a point called centre.

SECTION

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PARTS OF THE CIRCLE

PARTS OF THE CIRCLE

A line that "just touches" the circle as it passes by is called a TANGENT. A line that cuts the circle at two points is called a SECANT. A line segment that goes from one point to another on the circle's circumference is called a CHORD. If it passes through the center it is called a DIAMETER. The RADIUS of a circle is the length of the line from the center to any point on its edge.A part of the circumference is called an ARC.

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RELATIVE POSITION OF TWO CIRCLES

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USING THE COMPASS

CONSTRUCTING CIRCLES WITH A COMPASS

CONSTRUCTING CIRCLES WITH A COMPASS

CIRCLES ON CIRCLES

CIRCLES ON CIRCLES

USING CIRCLES TO DRAW OTHER FIGURES

FAMILIAR FIGURES IN THE SEVEN-CIRCLE PATTERN

FAMILIAR FIGURES IN THE SEVEN-CIRCLE PATTERN

Dividing a segment into several equal parts

We use Thales theorem to divide a given line segment into a number of equal parts with compass and straightedge or ruler. By using a compass and straightedge construction, we do this without measuring the line.