This material is a collective work, conceived, designed and created by the Editorial department at Santillana, under the supervision of Teresa Grence. WRITERS Karen Ballesteros Juan Carlos Taravillo Vivian Mitchell CLIL CONSULTANT Ángel Mentxaka ILLUSTRATORS Diomedes Guilombo Carlos Alberto Salas Juan Carlos Taravillo Cristina Vidal EDITORS Elena Alfonso Dave Wile EDITORIAL MANAGERS Nuria Corredera Montserrat Herrero PROJECT DIRECTOR Lourdes Etxebarria BILINGUAL PROJECT DIRECTOR Margarita España Technical drawing I SECONDARY Level Visual arts Design & Create audio available santillana.es/clil
P r a c t i s e These activities enable you to put into practice what you have learned in the unit. By doing these worksheets, you will improve your personal, social and learning to learn competence and digital competence. Ga l l e r y This section further develops your knowledge of technical drawing. Some additional information about the use of technical drawing in other areas is also included. In addition, you will also develop your personal, social and learning to learn competence and citizenship competence. Con t e n t The contents of the unit are introduced with examples that show you step-by-step how to draw geometric constructions. These pages are intended to develop your mathematical competence and competence in science, technology and engineering. C r e a t e These activities allow you to apply and to show what you have learned about the subject. By doing these worksheets, you will improve your entrepreneurship competence and cultural awareness and expression competence. Technical drawing I Technical drawing I is organised into seven units, which aim to develop technical drawing skills. Each unit contains the following sections: 7 Re gu l a r po l ygon s B X M C D E Y F A J K GALLERY In nature there are many things that are shaped like regular polygons. One example is the honeycomb that is made by bees. A polygon is a flat shape bounded by three or more segments. It is regular when all the sides and all the angles are equal. Elements of a polygon The elements of a polygon are the sides, vertices, interior angles and diagonals. For example, polygon ABCDEF has these parts: • Sides: AB, BC, CD, DE, EF and FA. • Vertices: A, B, C, D, E and F. • Interior angles: Â, Bˆ , Cˆ , Dˆ , Eˆ and Fˆ. • Diagonals: these are segments that connect two non-consecutive vertices. In a regular polygon, the apothem is the segment that connects the centre of the regular polygon to the midpoint of each side. All regular polygons can be inscribed in a circumference called a circumscribed circumference. Also, a circumference can be inscribed in all regular polygons and the radius is equal to the apothem. This is known as an inscribed circumference. Circumscribed circumference Inscribed circumference A B F C D E d f e m apothem Construct a triangle and a hexagon, given the circumscribed circumference Step 1. Draw the diameter of the circumference XY. Step 2. Draw the perpendicular bisector of the diameter XY. Where it intersects the circumference, label the points A and D. Step 3. Use centre point A and the length of the previous radius. Draw an arc that intersects the circumference at points B and F. Step 4. Use centre point D and the same radius. Draw an arc that intersects the circumference at points C and E. Step 5. Draw the segments AB, BC, CD, DE, EF and FA to form a regular hexagon. Step 6. Join points A, C and E to form an equilateral triangle. Technical Drawing I 51 ES0000000135172 175028_CDNO_DIB_TEC_Niv_I_ESO_Serie blanca_102752.indd 51 29/1/22 13:5356 CREATE Draw a landscape using parallel and perpendicular lines. Then colour it with felt-tip pens. 10 ES0000000135172 175028_CDNO_DIB_TEC_Niv_I_ESO_Serie blanca_102752.indd 10 29/1/22 13:5425 Draw parallel lines. PRACTISE 0 1 2 3 4 5 6 7 8 9 10 60º 0 1 2 3 4 5 6 7 8 9 10 90º 0 1 2 3 4 5 6 7 8 9 10 30º 0 1 2 3 4 5 6 45º Technical Drawing I 7 ES0000000135172 175028_CDNO_DIB_TEC_Niv_I_ESO_Serie blanca_102752.indd 7 29/1/22 13:5435 7 Re gu l a r po l ygon s B X M C D E Y F A J K GALLERY In nature there are many things that are shaped like regular polygons. One example is the honeycomb that is made by bees. A polygon is a flat shape bounded by three or more segments. It is regular when all the sides and all the angles are equal. Elements of a polygon The elements of a polygon are the sides, vertices, interior angles and diagonals. For example, polygon ABCDEF has these parts: • Sides: AB, BC, CD, DE, EF and FA. • Vertices: A, B, C, D, E and F. • Interior angles: Â, Bˆ , Cˆ , Dˆ , Eˆ and Fˆ. • Diagonals: these are segments that connect two non-consecutive vertices. In a regular polygon, the apothem is the segment that connects the centre of t e regular polygon to the midpoint of each side. All regular polygons can be inscribed in a circumference called a circumscribed circumference. Also, a circumference can be inscribed in all regular polygons and the radius is equal to the apothem. This is known as an inscribed circumference. Circumscribed circumference Inscribed circumference A B F C D E d f e m apothem Construct a triangle and a hexagon, given the circumscribed circumference Step 1. Draw the diameter of t circumference XY. Step 2. Draw the perpendicular bisector of the diameter XY. Where it intersects the circumference, label the points A and D. Step 3. Use c ntre point A a d the length of the previous radius. Draw an arc that intersects the circumference at points B and F. Step 4. Use centre point D and the same radius. Draw an rc that intersects the circumference at points C and E. Step 5. Draw the segments AB, BC, CD, DE, EF and FA to form a regular hexagon. Step 6. Join points A, C and E to form an equilateral triangle. Technical Drawing I 51 Listen to the audio files at santillana.es/clil
Contents UNITS 5 Tr i ang l e s 35 • Definition and classification of triangles • Notable lines and points of a triangle • How to construct triangles: given three sides; and given two sides and the angle they form • Construct figures with triangles 6 Quad r i l a t e r a l s 43 • Definition and classification of quadrilaterals • How to construct parallelograms: construct a rhomboid and a diamond given its diagonals • Construct isosceles trapeziums given the sides and the height; construct trapeziums given one of the sides, the diagonals and the height; and construct trapezoids given the four sides and a diagonal • Construct figures and landscapes using quadrilaterals 7 Re gu l a r po l ygon s 51 • Elements of a polygon • How to construct a regular polygon: a triangle, a hexagon, a square and an octagon inscribed in a circumference • Construct decorative shapes with polygons F i na l a c t i v i t i e s 5 9 • An activity bringing together all the points covered in this book • Digital resources: draw a star with Inkscape • Create a design and add figures to it using Inkscape G l o s s a r y 6 3 • Technical drawing terms that are used in this material UNITS 1 Us i ng s e t s qua r e s 5 • Draw lines at angles of 30°, 45° and 60° • Draw parallel lines • Construct shapes with set squares • Use set squares to draw angles greater than 90° 2 Us i ng a c ompa s s 13 • Recommendations for using and looking after a compass • Draw perpendicular lines with a compass • Draw the perpendicular bisector of a segment • Draw a straight line parallel to another straight line • Divide a segment into equal parts • Construct figures with a compass 3 Ang l e s 19 • Definition and classification of angles • How to construct angles: make an exact copy of an angle, bisect an angle and trisect a right angle • Construct figures with a compass and set squares 4 Th e c i r c umf e r e n c e and t h e c i r c l e 27 • The circumference and its elements • The circle and its divisions • Constructions using a compass: a circumference that passes through three given points; a figure formed by arcs of a circumference; and decorative figures formed by circumferences
Instruments and recommendations for Technical drawing How to prepare the drawing instruments • Keep the pencils sharpened. • Clean the set squares and rulers before and after their use. • Sharpen the lead point of the compass to get clear and precise measurements. • Make sure the rubber has clean and sharp edges. The drawing process • Read the instructions carefully and refer to the images. • Remember that each step of the process is given in a logical order. • Draw the guidelines with a hard pencil (H), pressing lightly. • Complete the final drawing lines with a soft pencil (B). • Do not rub out the guidelines until the drawing is completely finished. Take note • Read the directions and instructions before starting the worksheet. • Sign your worksheets with your name. Use technical lettering. • Keep your desk and worksheets clean. Protractor French curve Set squares Rubber Pencil Coloured pencils T-square Compass Ruler Pencil sharpener 4
Set squares are templates in the form of a right-angled triangle. With the help of a ruler, they allow you to draw horizontal lines, vertical lines and lines at an angle to the horizon. There are two types of set squares: • The 45º set square has two angles of 45º and one right angle of 90º. This shape forms an isosceles triangle because two of its sides and two of its angles have the same measurements. • The 60º/30º set square has two acute angles of 60º and 30º, and one right angle of 90º. This shape forms a scalene triangle because all of its sides and angles have different measurements. Set squares are used to form angles of different sizes. To do this, you place the T-square horizontally and put the set squares in the positions you can see on the right. 1 Us i ng s e t s qua r e s 0° HORIZONTAL 0° HORIZONTAL 15° 15° 30° 45° 60° 75° 30° 45° 60° 75° 15° 15° 30° 45° 60° 75° 30° 45° 60° 75° 90° VERTICAL 90° VERTICAL GALLERY Set squares can be made from various materials, but they are usually made of clear plastic. 90º 60º 30º 60º/30º set square 90º 45º 45º 45º set square Technical Drawing I 5
When constructing angles with the set squares, check they are in the correct position on the T-square. • To draw a straight line at an angle of 30°, use a 60º/30º set square. • To draw a straight line at an angle of 45°, use a 45º set square. • To draw a straight line at an angle of 60°, use a 60º/30º set square. Po s i t i on o f t h e s e t s qua r e s How t o d r aw a l i n e a t an ang l e o f 3 0 ° How t o d r aw a l i n e a t an ang l e o f 4 5 ° D r aw s t r a i gh t l i n e s a t ang l e s o f 3 0 ° , 4 5 ° and 6 0 ° 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 30º 0 1 2 3 4 5 6 45º 0 1 2 3 4 5 6 7 8 9 10 60º Co r r e c t I n c o r r e c t How t o d r aw a l i n e a t an ang l e o f 6 0 ° 6
Practise the activities on the previous page. 8
Construct this figure. Use a 45º set square. PRACTISE A A A Technical Drawing I 9
CREATE Draw a landscape using parallel and perpendicular lines. Then colour it with felt-tip pens. 10
To draw angles that are greater than 90º, position a 60º/30º set square and a 45º set square as follows: Us e s e t s qua r e s t o d r aw ang l e s g r e a t e r t han 9 0 ° With a 60º/30º set square and a 45º set square, you can also construct some regular polygons given one of their sides. For example, an equilateral triangle or an octagon. Re gu l a r o c t agon Equ i l a t e r a l t r i ang l e 105° 60° 60° 135° 135° C E D F C A B 150° 165° 135° Technical Drawing I 11
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