Question

prepare for angle relationships in triangles
① think about what you know about similarity and similar triangles. fill in each box. use words, numbers, and pictures. show as many ideas as you can.
in my own words
my illustrations
similar triangles
examples
non - examples
② are the triangles similar? explain.
10 m
20 m
15 m
12 m
16 m
8 m
lesson 7 describe angle relationships in triangles
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Explanation:

Step1: Recall similarity - ratio rule

For two triangles to be similar, the ratios of their corresponding sides must be equal.

Step2: Calculate side - to - side ratios

For the larger triangle with sides 10 m, 15 m, 20 m and the smaller triangle with sides 8 m, 12 m, 16 m.
The ratio of the first pair of corresponding sides: $\frac{10}{8}=\frac{5}{4}$.
The ratio of the second pair of corresponding sides: $\frac{15}{12}=\frac{5}{4}$.
The ratio of the third pair of corresponding sides: $\frac{20}{16}=\frac{5}{4}$.
Since the ratios of all corresponding sides are equal ($\frac{5}{4}$), the triangles are similar.

Answer:

Yes, the triangles are similar because the ratios of their corresponding sides are equal ($\frac{10}{8}=\frac{15}{12}=\frac{20}{16}=\frac{5}{4}$).

For the first part (the graphic organizer about similar triangles):

In My Own Words:

Similar triangles have the same shape but can be different in size. Their corresponding angles are equal and the ratios of their corresponding sides are the same.

My Illustrations:

Draw two triangles of different sizes but with the same angles. For example, two right - angled triangles, one small and one large, with angles 30°, 60°, 90°.

Examples:

Two equilateral triangles of different side lengths. One with side length 3 cm and another with side length 6 cm.

Non - Examples:

A right - angled triangle with side lengths 3, 4, 5 and an equilateral triangle with side length 5. They have different shapes and the side - length ratios are not consistent.