Warm-Up New Seats After you find your seat take a worksheet from the front table and work on the sides with the triangles Take out blue sheet when finished

Essential Questions What types of quadrilaterals are rep-tiles? Rectangles, Squares, Parallelograms, Rhombus, Some trapezoids measurement need to be specific for them to work How do rep-tiles show that a scale factors and areas of similar quadrilaterals are related? Ratio of Areas is Scale factor squared 2. Which types of triangles are rep-tiles? Explain. Right, Equilateral, Scalene, Isosceles, Take the larger triangle and you can divide it into smaller similar/congruent triangles How can you use scale factors to draw similar figures or to find missing side lengths in similar figures? Use the scale factor to multiply side lengths of one figure to make corresponding side lengths of another figure, know how perimeter and area of figures are related to get the scale factor Find scale factor by using corresponding sides and use this to multiple side of one figure to side of second figure How can you use similar triangles to find a distance that is difficult to measure directly? As long as triangles are similar, congruent corresponding angles the sides should be using the same scale factor, similar to question 3 for set up

Stretching and Shrinking Students will be able to use scale factor to determine distances, students will be able to find unknown heights using similar figures.

Investigation 4: Similarity and Ratios Students will explore and apply ratios and proportions when solving similar triangles.

Homework Investigation 4 We will work on these during class Page 90 A 1,3,4-7, 12,14,16,18 B 16,18,40,42,43,

4. 1 Ratio within Similar Parallelograms 4 4.1 Ratio within Similar Parallelograms 4.2 Ratios within similar Triangles What information does the ratio of adjacent side lengths within a rectangle give you? For a pair of triangles, if the measure of corresponding angles are equal, how can you use ratios of side lengths to determine whether or not the triangles are similar?

Terms Ratios comparison of two quantities, such as 2 lengths Equivalent Ratio’s like equivalent fractions, simplify down to the same value Proportion an equation setting two ratios equal Adjacent Sides two sides that meet at a vertex, one right after the other

Which rectangles are similar, why? Triangle A and B scale factor of 1/2 A and C scale factor of 3/4 C to B scale factor 2/3 For each of the rectangles find the ratio of the length of short side to the length of the long side? A: 3/5 B: 3/5 C: 3/5 D: 3/10 What do you notice about the ratios of sides for the similar rectangles? Non Similar? If rectangles are similar then the ratio of sides are the same

F and G, scale factor is 4/5 For each parallelogram find the ratio of lengths of long side to the length of short side, how do they compare? All are 4/5 If you find the ratio of adjacent sides in a rectangle or parallelogram and this ratio is equivalent to corresponding sides in another, are they similar? Rectangles yes Parallelogram, check for congruent angles, if similar then yes ratios are the same, if ratios are the same not necessarily are the figures similar

Ratios of Similar Triangles We just looked at ratios of sides in parallelograms, do you think this will hold true for triangles? Test it.

Essential Questions What information does the ratio of adjacent side lengths within a rectangle give you? It helps you determine which rectangles or parallelograms are similar For a pair of triangles, if the measure of corresponding angles are equal, how can you use ratios of side lengths to determine whether or not the triangles are similar? if the ratio of adjacent corresponding sides of one triangle are the same as another the triangles are similar

Problems

Warm Up

4.3 Finding Missing parts 4.4 Using Shadows to find height If two shapes are similar, how can you use information about the shapes to find unknown side lengths, perimeters and areas? How can you use similar triangles to estimate the heights of tall objects?

Set up and solve for missing side using scale factor Set up and solve for missing side using scale factor. Set up and Solve for missing side using rations/proportions.

Set Up Using scale factor Find scale factor between two figures Multiple scale factor by known side to get corresponding side Scale factor >1 S to L Scale factor <1 L to S Remember they are recipricals Using Ratios Find ratio of adjacent sides of one triangle Set equal to corresponding sides of second triangle Solve for unknown, think of multiplication and addition how do you rewrite fact families

Shadows and Similar Triangles

Process Use similar triangles to set up ratios of corresponding sides and set equal to each other Draw a picture Measure your height Measure your shadow Measure object shadow Write measurement in pictures Set up and Solve

Problem

If sunny we will do a lab You and your group will be given an object to measure

Essential Questions If two shapes are similar, how can you use information about the shapes to find unknown side lengths, perimeters and areas? You can use ratio of sides to help determine if shapes are similar You can then set up a scale factor to help relate areas and perim How can you use similar triangles to estimate the heights of tall objects? Set up similar triangles and calculate unknown corresponding lengths