Exercise 3 Page 441

We are asked to determine whether $△ J K L$ or $△ R S T$ are similar to $△ A B C .$

Let's first consider $△ J K L$ and then $△ R S T .$

Triangles $△ J K L$ and $△ A B C$

On the diagram we are given the lengths of all of the sides in each triangle. To determine if the triangles are similar we can use the Side-Side-Side (SSS) Similarity Theorem.

Side-Side-Side (SSS) Similarity Theorem
If the corresponding side lengths of two triangles are proportional, then the triangles are similar.

Let's identify the corresponding sides of the triangles on the diagram.

Now, we can calculate the ratios of the corresponding sides and see if they are the same.

Shortest Sides : Longest Sides : Remaining Sides : \frac{B C}{K L} \frac{A C}{J L} \frac{A B}{J K} = = = \frac{8}{7} \frac{1 2}{1 1} \frac{7}{6}

As we can see, all three ratios are different. Therefore, the corresponding sides are not proportional and the triangles are not similar.

Triangles $△ R S T$ and $△ A B C$

Similarly, let's start with identifying the corresponding sides of these triangles.

We can again calculate the ratios of the corresponding sides and see if they are the same.

Shortest Sides : Longest Sides : Remaining Sides : \frac{B C}{S T} \frac{A C}{R T} \frac{A B}{R S} = = = \frac{8}{4} \frac{1 2}{6} \frac{7}{3 . 5} = = = 222

We can see that the all two ratios are equal, so the corresponding sides are proportional. Therefore, by the SSS Similarity Theorem we conclude that the triangles are similar.

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Triangles $△ J K L$ and $△ A B C$

Triangles $△ R S T$ and $△ A B C$

Exercise 3 Page 441

Hints

Check the answer

Practice exercises

Asses your skill

Triangles △JKL and △ABC

Triangles △RST and △ABC

Triangles $△ J K L$ and $△ A B C$

Triangles $△ R S T$ and $△ A B C$