Similar Triangles

Warmup

Create three different expressions that are each equal to 20. Each expression should include only these three numbers: 4, -2, and 10.

(1.) First expression:

(2.) Second expression:

(3.) Third expression: expression:

Activity #1

Create a Triangle with a Given Angle.

• Create a triangle using three ‘pieces of pasta’ and angle A. Your triangle must include the angle you were given, but you are otherwise free to make any triangle you like.

After you have created your triangle,……

Measure the angles to the nearest 5 degrees using a protractor and record these measurements.

• Now use more ‘pasta’ and angles A, B, and C to create another triangle.

After you have created your triangle,……

(1.) Measure the angles to the nearest 5 degrees using a protractor and record these measurements.

(2.) Compare the two triangles you created.

(a.) What is the same?

(b.) What is different?

(c.) Are the triangles congruent?

(d.) How did you decide if they were or were not congruent or similar?

Activity #2

Create Similar Triangles.

Here is triangle PQR.

• Break a new piece of ‘pasta’, different in length than segment PQ. ​
• Move point S to create this new segment.​
• Create another piece of pasta by checking ‘piece 2’ with one end at S, and make an angle congruent to ∠PQR. ​
• Create another piece of pasta by checking ‘piece 3’ on top of line  PR with one end of the pasta at P. ​
• Call the point where the two full pieces of pasta meet T. 

(1.) Is your new pasta triangle  similar to  ΔPQR ? Explain your reasoning.

(2.) If your broken piece of pasta were a different length, would the pasta triangle still be similar to ΔPQR ? Explain your reasoning.

Activity #3

Find Similar Triangles in a Composite Figure.

The diagram in the applet below has several triangles that are similar to triangle DJI.

• Study all the triangles and answer the questions that follow.

(1.) Three different scale factors were used to make triangles similar to  DJI. In the diagram, find at least one triangle of each size that is similar to DJI.

(2.) Explain how you know each of these three triangles is similar to DJI.

(3.) Find a triangle in the diagram that is not similar to DJI.

(4.) Figure out how to draw some more lines in the pentagon diagram to make more triangles similar to DJI.

Challenge #1

Quadrilaterals ABCD and EFGH have four angles.

The angles measure  240°, 40°, 40°  and  40°. Do ABCD and EFGH  have to be similar?

Challenge #2

In each pair, some of the angles of two triangles in degrees are given. Use the information to decide if the triangles are similar or not. Explain how you know.

(1.) Triangle A: 53, 71, ___; Triangle B: 53, 71, ___

(2.) Triangle C: 90, 37, ___; Triangle D: 90, 53, ___

(3.) Triangle E: 63, 45, ____; Triangle F: 14, 71, ____

(4.) Triangle G: 121, ___, ___; Triangle H: 70, ___, ___

Challenge #3

In the figure, line BC is parallel to line DE.

Explain why ΔABC is similar to ΔADE.