The sides of a triangle measure 5,6 and 8 inches. Find the sides of a similar triangle if the si

step 1 For this problem, we are looking at two triangles. First, we have a triangle with sides five, si

The sides of a triangle measure 5,6 and 8 inches. Find the...

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Key Concepts

Corresponding Sides

Corresponding sides in similar triangles are the pairs of sides that lie opposite equal angles. The lengths of these sides maintain a constant ratio in all similar triangles, which is used to solve for unknown measurements when one or more side lengths are provided.

Scale Factor

The scale factor is the ratio that relates the lengths of corresponding sides in similar figures. It is determined by dividing a side length in one triangle by its corresponding side length in another triangle, and it is then applied to all other sides to generate the dimensions of the similar figure.

Similar Triangles

Similar triangles are triangles that have the same shape, meaning their corresponding angles are equal and their corresponding sides are proportional. This concept allows one to determine unknown side lengths by using the ratios that relate the sides of one triangle to another, regardless of their overall size.

Transcript

00:01 For this problem, we are looking at two triangles.

00:04 First, we have a triangle with sides five, six, and eight.

00:08 So i'm just going to draw ourselves a little triangle.

00:09 It's not necessarily to scale, but five, six, and eight.

00:14 And then we're told we have a similar triangle.

00:16 Now, this is going to be a little bit bigger.

00:18 We're told that the corresponding side to the six inches on the first triangle is nine inches on the second.

00:25 And we have two other sides that we don't know, a and b.

00:30 So how do we find the sides on this similar triangle? remember, a similar triangle means that i have taken my original triangle and either expanded it or shrunk it proportionately.

00:43 So as i look at these, if one side was twice as big as the other in this triangle, it's still going to be twice as big as the other in this triangle, just instead of being perhaps two and four, maybe now it's 20 and 40.

00:55 So even if the sides are different, proportionately they have remained consistent.

01:02 So let's take a look.

01:04 I know that this red side and this red side correspond to each other.

01:11 And i'm just going to mark in my colors the sides that correspond.

01:16 So i can set up a proportion.

01:18 I can say, let's go small to big...

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