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

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Presentation transcript:

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

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

Pythagorean Theorem We know how to find missing edges of triangles now. Let’s 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.

Answers (Question 1)

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

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

CirclesCircles Let’s review some parts of the circle. Question types with circles are simple, but it’s important that we understand the vocabulary.

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 doesn’t 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.

AnswersAnswers

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… Let’s find the hypotenuse.

Answers - Easy Answers - Medium Answers - Hard

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.