Title:

Title: SIMILARITY: Introduction

I Unit: Similarity

II. Goals:

1) TLW be able to define similar figures.
2) TLW recognize similar figures.
3) TLW be able to identify angle measures based on figures' similarity.
4) TLW be able to find side lengths based on figures' similarity.
5) TLW be able to define and identify the Scale Factor.

III. Instructional Objectives:

1) TLW state the two conditions required for figures to be similar.
2) TLW match figures with a similar figure with 90% accuracy.
3) TLW calculate the measure of angles based on the angle measures of a similar figure with 90% accuracy.
4) TLW calculate the lengths of a figures' sides based on the length of a similar figure's sides with 90% accuracy.

IV. Student Entry Level: Familiar with congruence and ratios, but no knowledge of similarity.

V. Desired Mastery Level: 90%

VI. Set:

If you remember from the distant past, also known as a few weeks ago, we learned a lot of stuff about congruency. We learned what it means for figures to be congruent.

Congruent figures were basically the same shape and size. Well, now we're going to go a little beyond that. We're going to talk about things that are the same shape but different sizes.

Who in here will admit to ever watching the Discovery Channel? (pause for any response) Have you ever seen the show "Movie Magic"? It's a fantastic show which goes into all the different special effects from the movies. They'll show things like the making of "Attack of the 50 Foot Woman" or "Honey, I Shrunk the Kids" where they use two different versions of everything; one big one and one little one. The things are exactly the same as much as possible, they're just different sizes.

Well, that's the concept we're working with today. We're going to look at things that look the same as far as shape is concerned, but are different where size is concerned.

VII. Instructional Procedures:

Figures that are the same shape but different sizes are said to be similar.

In order to be considered "having the same shape", two conditions have to be met.
1) corresponding angles are congruent
2) corresponding sides are proportional

Corresponding angles are congruent

naming congruent triangles according to which vertices matched between the triangles

(quick example -- congruent triangle names)

those were corresponding angles, like CPCTC [Corresponding Parts of Congruent Triangles are Congruent]

EXCEPT: now these are just the angles
(example -- big & small quadrilaterals)
(counter example -- change drawing on one quad)
(example -- pentagons -- find angle measures) ** 160, 60, 75, 125, 120

Corresponding sides are proportional

(example -- triangles 2X sides)

notice that these sides are all exactly twice as long as the corresponding sides of the other figure

scale factor - the ratio of the corresponding sides of similar polygons
(last ex. SF=2)
(example -- book example)

if not...shape changes

(counter example -- square & rectangle) - side ratios
(counter example -- square & rhombus) - angle measures
(example -- congruent quads)

VIII. Checking for Understanding:

(example -- triangles -- them tell me what to do)
(example -- quads -- start w/ similarity & list relations)

IX. Supervised Practice: Assignment: (subject to change)

p. 266 # 1-30, 32-38 even

X. Closure: Remind class that there will be a quiz tomorrow.

ratios & proportions
what similar polygons are
what 2 things make polygons similar
scale factor
find angle measures & side lengths based on similarity

XI. Independent Practice: p. 268 "Quiz" #1-12

XII. Lesson Evaluation: Complete after giving lesson.

XIII. Materials and their Use:

Text book - homework problems, definitions, example
dry erase board - visual demonstration
Overhead - visual demonstration