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1. When you classify triangles you can do it according to the angles or according to the sides.
1.1 Classification on the basis of the angles of a triangle:Are you able to complete the following?
a) Acute-angled triangles are triangles with
b) Right-angled triangles have
c) Obtuse-angled triangles have
1.2 Classification on the basis of the sides of the triangle:Are you able to complete the following?
a) An isosceles triangle has
b) An equilateral triangle has
c) A scalene triangle's
2. Are you able to complete the following theorems about triangles? Use a sketch to illustrate each of the theorems graphically.
THEOREM 1:
Sketch:
THEOREM 2:
Sketch:
3. Constructing triangles:
Remember this:
3.1 Construct $\Delta $ PQR with PQ = 7 cm, PR = 5 cm and $\stackrel{\u02c6}{P}$ = 70°.
a) Sketch:
b) Measure the following:
1. QR = ........ 2. $\stackrel{\u02c6}{R}$ = ........ 3. $\stackrel{\u02c6}{Q}$ = ........ 4. $\stackrel{\u02c6}{P}+\stackrel{\u02c6}{Q}+\stackrel{\u02c6}{R}=$ ........
3.2 Construct $\Delta $ KLM , an equilateral triangle. KM = 40 mm, KL = LM and $\stackrel{\u02c6}{K}$ = 75°.Indicate the sizes of all the angles in your sketch.
Sketch:
Practical exercise: Making you own tangram.
1. Cut out a cardboard square (10 cm x 10 cm).
2. Draw both diagonals, because they form part of the bases of some figures.
3. Divide the square in such a way that the complete figure consists of the following:
3.1 two large equilateral triangles with bases of 10 cm in length;
3.2 two smaller equilateral triangles, each with base 5 cm in length;
3.3 one medium equilateral triangle with adjacent sides 5 cm in length;
3.4 one square with diagonals of 5cm;
3.5 one parallelogram with opposite sides of 5 cm.
4. Now trace the largest triangle of your tangram in your workbook as a right-angled triangle.
5. Arrange the seven pieces to form a square and place this on the hypotenuse of the traced triangle.
6. Now arrange the two largest triangles to form a square and place this on one of the sides adjacent to the right angle of the traced triangle.
7. Arrange the remaining pieces to form a square and place this on the other adjacent side.
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