the lengths of the sides of four triangles are listed as follows. which two triangles are similar? explain.
a~ 5 cm, 6 cm, 8 cm
b~ 6 cm, 7 cm, 8 cm
c~ 8 cm, 10 cm, 12 cm
d~ 12 cm, 15 cm, 18 cm
any ration can be reduced by dividing out a common factor .
so ...
c) 8:10:12 = 4:5:6
d) 12:15:18 = 4:5:6
So, what do you think?
thank you!
To determine which two triangles are similar, we need to compare the ratios of their corresponding side lengths. If two triangles have the same ratios for their corresponding side lengths, then they are similar.
Let's compare the ratios:
For Triangle a:
- Ratio of the lengths of the first two sides (5 cm and 6 cm) is 5/6.
- Ratio of the lengths of the first and third sides (5 cm and 8 cm) is 5/8.
- Ratio of the lengths of the second and third sides (6 cm and 8 cm) is 6/8.
For Triangle b:
- Ratio of the lengths of the first two sides (6 cm and 7 cm) is 6/7.
- Ratio of the lengths of the first and third sides (6 cm and 8 cm) is 6/8.
- Ratio of the lengths of the second and third sides (7 cm and 8 cm) is 7/8.
For Triangle c:
- Ratio of the lengths of the first two sides (8 cm and 10 cm) is 8/10.
- Ratio of the lengths of the first and third sides (8 cm and 12 cm) is 8/12.
- Ratio of the lengths of the second and third sides (10 cm and 12 cm) is 10/12.
For Triangle d:
- Ratio of the lengths of the first two sides (12 cm and 15 cm) is 12/15.
- Ratio of the lengths of the first and third sides (12 cm and 18 cm) is 12/18.
- Ratio of the lengths of the second and third sides (15 cm and 18 cm) is 15/18.
By comparing the ratios of the corresponding side lengths, we can see that triangles a and b have the same ratios for their corresponding side lengths (5/6, 5/8, 6/8, and 6/7, 6/8, 7/8 respectively). Therefore, triangles a and b are similar.