Question

spiral review
problems 6 - 9: triangle def is a scaled copy of triangle abc. for each of the parts of triangle abc, identify the corresponding part for triangle def.

1. angle abc
2. angle bca
3. side ac
4. side ba
5. draw a figure that has an area of 8 square units. try to make a figure no other student will think of.
6. imagine a scaled copy of your figure that uses a scale factor of 2. what would be the area of the scaled copy?
7. make a scaled copy of your original figure using a scale factor of 0.5. what is the area of the new figure?

Explanation:

Step1: Identify corresponding parts for similar - triangles

For similar triangles, corresponding angles and sides are in the same relative position.

Step2: Answer questions 6 - 9

1. Angle $ABC$ corresponds to angle $DEF$.
2. Angle $BCA$ corresponds to angle $EFD$.
3. Side $AC$ corresponds to side $DF$.
4. Side $BA$ corresponds to side $ED$.

Step3: Draw a figure for question 10

One possible figure is a rectangle with length 4 units and width 2 units (there are many other possible non - standard figures).

Step4: Calculate area for scaled - figure in question 11

If the scale factor is $k = 2$, and the original area is $A_1=8$ square units. The area of the scaled figure $A_2$ is given by the formula $A_2=k^{2}A_1$. So $A_2 = 2^{2}\times8=32$ square units.

Step5: Calculate area for scaled - figure in question 12

If the scale factor is $k = 0.5$, and the original area is $A_1 = 8$ square units. Using the formula $A_2=k^{2}A_1$, we have $A_2=(0.5)^{2}\times8 = 2$ square units.

Answer:

1. Angle $DEF$
2. Angle $EFD$
3. Side $DF$
4. Side $ED$
5. (One possible answer) A rectangle with length 4 units and width 2 units
6. 32 square units
7. 2 square units