# Relationship between perimeters of similar triangles

### Is side length & perimeter proportional? (video) | Khan Academy

The perimeter of two similar triangles ABC and PQR is 36 and Perimeter of ΔPQR = 24 units and PQ = 10 units. Since Hence AB is 15 units. Use these polygons to explore the relationships between side, perimeter, and area ratios. This lesson investigates the relationships between the area and perimeter of similar . Does the relationship you determined for similar triangles also work for .

And what I want to think about here is whether the perimeter of the square is proportional to the length of a side of the square.

So let's think about it a little bit. I'm going to draw a table, so let me make some columns here. So there you have that, we have that, and we'll make three columns and on the first column we're going to think about the Side length. Side length, and that's measured as x. And in the next column I want to think about the Perimeter. Well what is that? That's going to be x plus x plus x plus x which is, of course, four x. And then I want to think about the ratio. The ratio between Perimeter, Perimeter and Side length.

So let's see, when the Side length is equal to one, what's the Perimeter? It's going to be four times one. One plus one plus one plus one. It's going to be four.

And what's our ratio? It's going to be four to one which, of course, is equal to four. Now what if the Side length is two? Have students write in any missing dimensions. Lead them to determine the missing dimensions from the given ones.

## How does scale factor affect the areas and perimeters of similar figures?

Give each group or student a data log sheet for rectangles. Have students use the definition of similarity to verify that the three rectangles are similar to each other. The angles are all right angles so the emphasis should be on verifying the proportionality of the corresponding sides. Have students identify the scale factor for each set of two rectangles. These scale factors should be recorded on the log sheet.

Now have the students complete the Perimeter and Area calculations and enter their results on the log sheet.

### Area and Perimeter of Similar Polygons ( Read ) | Geometry | CK Foundation

Have students answer the figure specific questions by referring to the data in the appropriate chart on their data sheet. Give each group or student a data log sheet for triangles. Repeat steps for the triangles. How will students organize and interpret the data collected during the investigation?

Ask students to study their answers to the questions on their lab sheets. Their goal will be to write a rule that relates the perimeter and area of similar polygons to the scale factors of those polygons.

Each group should generate its own rule, and then test the rule on the three rectangles and three triangles in their logs. Does the rule they generated work for all six figures? If not, ask students to rework the rule and try again. Emphasize that the rule will only be useful if it works for all figures, all the time!

In this step, students are just putting the last statement completed on the triangle log sheet into their own words. What will the teacher do to bring the lesson to a close?

## Area and Perimeter of Similar Triangles

How will the students make sense of the investigation? Teacher returns to the similar rectangles question from the "hook.

Tell them to write their explanation in terms of the scale factor of the rectangles. The teacher should be sure that all students realize that if two 2D figures have a scale factor ofthen their perimeters will differ by a factor ofand their areas will differ by a factor of. Summative Assessment Teacher will draw a new set of similar rectangles and triangles on the board.

### How does scale factor affect the areas and perimeters of similar figures? -

Ask students to identify the scale factors that relate the similar rectangles and the scale factor that relates the similar triangles. Next, ask for volunteers to predict how the area and perimeter of figures will change in relation to their scale factors; e.

Have them justify that the triangles they have drawn are indeed similar. Then have them identify the scale factor that relates the two triangles. Formative Assessment Examine the four triangles in the figure below. Downloadable attachment Measure all three sides and all three angles of each triangle.

Make three observations about the measures you found.

What is different about certain measures in the third triangle? Teacher looks for observations that capture the following ideas: The two triangles in the first row have corresponding side lengths that are the same, and their corresponding angles are the same.

The triangle in the second row has sides that are twice as long as the corresponding sides of either triangle in the first row, but corresponding angles are unchanged. The angles of the triangle in the third row are different from the corresponding angles of triangles in the first two rows. In addition, its proportions are different from the triangles in the first two rows. Teacher elicits the definitions of similarity and congruence. Feedback to Students Students will receive immediate feedback when answering questions.

The teacher will look for specific areas of difficulty such as: Students may not realize that similarities preserve shape, but not size. Angle measures stay the same, but side lengths change by a constant scale factor. Students may incorrectly apply the scale factor.

**Area of Similar Triangles**