If two figures, F and G, have the same shape, but are not necessarily the same size, we say they are SIMILAR. Mathematically, we write this this way;

F ~ G

1. If two figures F & G, are congruent, are they always, sometimes, or never similar ?
2. If two figures F & G, are similar, are they always, sometimes,or never congruent ?
3. If F @ G and G ~ H, are F and H always, sometimes,or never similar ?
4. If F ~ G and G ~ H are F and H always, sometimes,or never similar ?
5. If F @ G and G ~ H, are F and H always, sometimes,or never congruent ?
6. Photographic enlargements made from the same negative are similar. Discuss why this is so.

Follow the directions to this activity and answer the questions about the figures you've drawn.

7. Use a protractor and ruler to draw DABC (start by drawing AB) with ÐA = 40°, ÐB = 60°, and AB = 6cm.  Now draw   DDEF with ÐD = 40° , ÐE = 60° and DE = 12 cm.

• Is DDEF ~ DABC, if so, then explain why ?

8. Set up a coordinate plane (X & Y axis) and plot the following points: A(5, 2), B(1,2), C(5,6), D(3, -2), E(6, -5), and F(2, -6). Connect points A, B, and C to form DABC, and connect points D, E, and F to form DDEF.

• Then use the distance formula (showing all your work) to calculate the length of each side of DABC & DDEF.
• What kind of triangle is DABC ? Justify your answer.
• What kind of triangle is DDEF ? Justify your answer.
• Are these triangles similar ? Explain.

9. Discuss with your partner or group how to determine whether two figures are similar. Then write a sentance or two that summarizes what is necessary for two figures to be similar so that a friend who is not in this class would understand similarity.