Step-by-step explanation:
1. AB corresponds to XY
2. BC corresponds to YZ
3. AC corresponds to XZ
4.
Corresponding Sides
AB corresponds to DE
AC corresponds to DF
BC corresponds to EF
Ratios:
3:6
4:8
5:10
They are similar because 3:6, 4:8, and 5:10 are all equal to 1:2
5.
Corresponding Sides
JK corresponds to MN
KL corresponds to NP
LJ corresponds to PM
Ratios:
5:6
5:6
7:8
They are NOT similar because both 5:6 ratios are equal to 1:1.2 and the 7:8 ratio is equal to about 1:1.4
6. They are NOT similar because no matter how you rotate the scale triangle (the larger one), it is not the same shape as the original triangle (the smaller one.)
7.
Corresponding Sides
YX corresponds to UV
XZ corresponds to VW
ZY corresponds to WU
Ratios:
4:5
4:5
4:5
They are similar because each ratio is 4:5. Even though they do not look similar, if you flip over the first triangle in the pair, it will line up correctly.
8.
Ratios:
2:6 (Top)
4:8 (Left Side)
4:8 (Right Side)
2:6 (Bottom)
They are NOT similar because the 2:6 ratios equal 1:3 and the 4:8 ratios equal 1:2.
9.
Ratios:
7:10.5 (Slanted Top)
3:4.5 (Slanted Side)
6:9 (Side)
4:6 (Bottom)
Simplifying...
7:10.5 = 1:1.5
3:4.5 = 1:1.5
6:9 = 1:1.5
4:6 = 1:1.5
Answer
They are similar because the ratios 7:10.5, 3:4.5, 6:9, and 4:6 are all equal to 1:1.5
Note:
If I missed any parts please let me know! I can clarify if needed. Also sorry I responded so late!
