Similar triangles are triangles that have the same shape but different sizes. If they have two similar angles, then it is automatically similar. But when you have 2 triangles and they have angles of similarity but they are different sizes it would be triangles like:
Step 1: To find what the length is, make a ratio. Put the sides that are the same over each other.
Step 2: Put 3 over 6 and x over 12.
Step 3: Cross multiply. You should come out with 6x over 36.
Step 4: Divide that by 6 for each one and you should get x over 6. That means x=6.
Questions:
1.) Find the value of X and Y and also the angle of P.
2.) Prove that ABE is similar to CDE.
3.) Are the triangles below similar? Why or why not?
Answer Key:
1.) Angle P is corresponding to Angle S so that means P = 86º. To find x use the ratio 4 over 6 and x over 9. When you cross multiply, it should come out to 6x over 36. So x=6. To find why use the ratio 4 over 6 and 7 over y. When you cross multiply, it should come out to 4y over 42. That means y=10.5.
2.) Angle ABE and CDE are similar because we already know for a fact that E is similar. Also we know that C≈A since they have the congruent symbol on the angles. Since two of the angles are similar, that means the last one has to be the same too.
3.) The triangles below are similar. Angle L and V are already congruent as we can see in the picture. Use these ratios below to know that they are similar.
UV 9 3 VW 15 3
-- = -- = - -- = -- = -
KL 12 4 LM 20 4
No comments:
Post a Comment