Slideshow 40, Mathematics Mr Richard Sasaki, Room 307

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Slideshow 40, Mathematics Mr Richard Sasaki, Room 307 Similar Shapes Slideshow 40, Mathematics Mr Richard Sasaki, Room 307

Objectives Review how to calculate unknowns in ratios Understand how to find missing lengths for similar shapes Calculate missing lengths for similar triangles

Ratios Ratios compare two or more numbers and are written in the form 𝑥 :𝑦 where 𝑥 and 𝑦 are numbers. Example If both 4:6 and 10: 𝑥 are in the same ratio, calculate 𝑥. 4:6 x 2.5 x 2.5 10: 15 Easy stuff, try the first worksheet!

Answers Try the activote exercise.

Question 1 B A 5cm : 7.5cm 2 : 3 6cm : ____ x 3 x 3 9cm These two triangles are similar. 7.5cm B 5cm A 6cm ? Triangle A and B have heights 5cm and 7.5cm respectively. If triangle A has base 6cm, what is the base of triangle B?

Question 2 3cm 3cm 3cm 10cm 9cm 1cm 1. Split the rectangle into 2 similar rectangles that are not congruent. 2. Prove that the flashing length is 3cm using the method in Question 1.

Answers 9 cm2 No as only one has an obtuse angle. 4

Dissection Any triangle can be split into four congruent triangles (similar to the original).

Puzzle Watch the picture above carefully…

Puzzle Watch the picture above carefully… Where did the empty square come from?

Puzzle Here it is slower…

Solution

No!! Solution Are the two triangles similar? 5 : 2 8 : 3 1 : 2/5 1 : 3/8 1 : 0.4 1 : 0.375

Answers Yes, show this with a ruler and measure. The lines make an isosceles triangle. No, the parallelograms are not similar. 2. Yes 3. They are congruent.

Counting Answers

Counting Answers