Question

unit 1 lesson 5 additional practice problems

1. triangles a, b, c, and d are scaled copies of one another. for each pair, decide if the scale factor from one to the other is greater than 1, equal to 1, or less than 1.

a. from a to b
b. from a to c
c. from d to a
d. from d to b
e. from c to a
f. from c to d
g. from b to c

Explanation:

Step1: Recall scale - factor concept

The scale factor \(k\) from a pre - image to an image is given by \(k=\frac{\text{length of a side in the image}}{\text{length of the corresponding side in the pre - image}}\). If the image is larger than the pre - image, \(k > 1\); if the image is the same size as the pre - image, \(k = 1\); if the image is smaller than the pre - image, \(k<1\).

Step2: Analyze from \(A\) to \(B\)

Since \(B\) is larger than \(A\), the scale factor from \(A\) to \(B\) is greater than \(1\).

Step3: Analyze from \(A\) to \(C\)

Since \(C\) is smaller than \(A\), the scale factor from \(A\) to \(C\) is less than \(1\).

Step4: Analyze from \(D\) to \(A\)

Since \(A\) is larger than \(D\), the scale factor from \(D\) to \(A\) is greater than \(1\).

Step5: Analyze from \(D\) to \(B\)

Since \(B\) is larger than \(D\), the scale factor from \(D\) to \(B\) is greater than \(1\).

Step6: Analyze from \(C\) to \(A\)

Since \(A\) is larger than \(C\), the scale factor from \(C\) to \(A\) is greater than \(1\).

Step7: Analyze from \(C\) to \(D\)

Since \(D\) is larger than \(C\), the scale factor from \(C\) to \(D\) is greater than \(1\).

Step8: Analyze from \(B\) to \(C\)

Since \(C\) is smaller than \(B\), the scale factor from \(B\) to \(C\) is less than \(1\).

Answer:

a. greater than 1
b. less than 1
c. greater than 1
d. greater than 1
e. greater than 1
f. greater than 1
g. less than 1