Identifying Scales and Ratios of Similarity Slideshow 32, Mathematics Mr. Richard Sasaki, Room 307

ObjectivesObjectives Recall some basic metric units for length Recall some basic metric units for length Understand how to use a given scale using ratio notation Understand how to use a given scale using ratio notation Recall necessary notation for similar shapes Recall necessary notation for similar shapes Understand how to find centres of enlargement Understand how to find centres of enlargement

UnitsUnits Let’s convert metric distances with units! Baby stuff! But firstly…

ScalesScales What is a scale? A scale is a key (a plan) that we follow throughout to make something smaller (or larger). Scales are used to make maps and enlarge and shrink appearances of objects. This image is the same size as my phone. This image has the dimensions halved. Note: Ratios are not used for enlargement.

Models and Scales Collectors models usually have a scale attached to them. These are called scale models.

Map Reading A map consistently follows the same scale so we can calculate distances between locations as the crow flies. (Without following roads, walkways etc.) Note: We always measure from centre to centre. This includes towns, other dwellings and structures Note: Scales should have no units. cm

AnswersAnswers This value decreases as the map scale is closer to real life.

Paper Size (Question 2)

NotationNotation Look at the statement below. This would be read as… Triangle ABC is congruent to Triangle XYZ. Triangle ABC is similar to Triangle XYZ. Congruent implies the same size and shape. Transposing, rotation and reflection are accepted. Similar implies the same proportions in size. The shape (angles) must be the same.

AnswersAnswers Well done if you remembered the line segment symbols! Don’t forget each of the following… Line Segment AB is written as. Line AB is written as. Ray AB (starting at A) is written as.

Similar Shapes As you all know, similar shapes all have… 1. Equal Angles 1. Edges all in the same proportion Like scales, similar shapes follow the same rules throughout.

Centre of Enlargement What on earth are they? A centre of enlargement is a central point for similarity. Two or more similar shapes can exist where one is a transformation of another. Example Look at the image below. If pentagon ABCDE is twice the distance of it’s transformation, write down the transformation’s scale.

Answers – Part 1

Answers – Part 2 No centre of enlargement The transformation is double the base and height.