Text of 2D Applications of Pythagoras - Part 1 Slideshow 41, Mathematics Mr. Richard Sasaki, Room 307

Slide 1

2D Applications of Pythagoras - Part 1 Slideshow 41, Mathematics Mr. Richard Sasaki, Room 307

Slide 2

ObjectivesObjectives Review polygon properties and interior angles Review circle properties Be able to apply the Pythagorean Theorem to other polygons, circles and graphs

Slide 3

Pythagorean Theorem We know how to find missing edges of triangles now. Lets apply this to other polygons. Oh wait, what is a polygon? A polygon is a 2D shape with straight edges only. We actually already did this, this is a review. Example Find the unknown value on the polygon below.

Slide 4

Answers (Question 1)

Slide 5

Answers (Question 2) We know an interior angles in a hexagon add up to.

Slide 6

Answers (Question 3) We know an interior angles in an octagon add up to. We have a 45-45-90 triangle.

Slide 7

CirclesCircles Lets review some parts of the circle. Question types with circles are simple, but its important that we understand the vocabulary.

Slide 8

CirclesCircles Example Consider a circle with radius 6 cm. The circle has a chord 8 cm long. Find the distance between the centre and the chord. Note: It doesnt matter where the chord is, as it is a fixed length, it is always the same distance from the centre. So it may as well touch the radius.

Slide 9

AnswersAnswers

Slide 10

GraphsGraphs Distances between points can be calculated, based on their coordinates. Note: The shortest distance between two points is always the of a triangle. hypotenuse Example We should visualize the triangle like or Lets find the hypotenuse.

Slide 11

Answers - Easy Answers - Medium Answers - Hard

Slide 12

FormulaeFormulae One of these will be provided in the exam, however you know how to do the questions without them anyway! Please bring a ruler, pencil and compass to the next lesson.