Mathematics 1 ESO – Unit 11 POLYGONS AND THE CIRCUMFERENCE extra activities
1 – Watch the video on “Triangles” and answer:
- a) What are the two ways to classify triangles?
- b) What are the three types of angles?
- c) How many acute angles has a triangle?
- d) How many right angles has a right triangle?
- e) What type of triangles have two equal sides?
- f) Can an equilateral triangle be an obtuse triangle? Why?
- g) If we add the three angles of a triangle, what is the total value?
2 – Watch the video on “Pythagorean Theorem” and answer:
- a) What theorem did professor Pogo use to calculate the length of the rope?
- b) What does the theorem say?
- c) What is the angle between the sidewalk and the meter?
- d) What length of rope we need if:
- I) Height of meter is 4 feet and distance to hydrant is 5 feet.
- II) Height of meter is 1 metre and distance to hydrant is 3 metres.
3 – Watch the video on “Circle Theorems, angles at the centre and circumference” and answer:
- a) Why x = 2y is the equation that relates angles at the centre and at the circumference?
- b) What is “x” in that equation?
- c) After watching the example at the video, solve this problem: “One of the lower angles of a triangle formed by an angle at the centre is 45°.
- I) What is the value of the angle at the centre?
- II) What is the value of the angle at the circumference?
4 – Watch the video on “Relationship Between a Circle and a Straight Line” and answer:
- a) When is the relation between a line and a circumference “external”?
- b) What is the difference between “tangent” and “secant” relative positions?
5 – Watch the video on “Labelling a circle” and answer:
- a) How do we call the perimeter of the circle?
- b) What is the difference between a chord and the diameter?
- c) Can a tangent line pass through the centre of the circle? Why?
- d) What two parts of the circle are areas? What is the difference between them?
- e) If the arc length is 1/8 of the length of the complete circumference, what is the angle between the two radii that form the arc?