Triangle I has sides with lengths 2 2/3 cm, 4 1/2 cm and 3 cm. Triangle II has sides with lengths 8 cm, 13 1/2 cm and 9 cm. Are these triangles similar? If yes, what is the ratio of correspondence?
Triangle 1:
2 2/3 : 4 1/2 : 3
= 16:27:18
triangle2:
8:13 1/2:9
= 16:27:18
yes they are similar
the ratio of correspondence is 1:3
(I took the last numbers 3:9 = 1:3)
To determine if two triangles are similar, we need to compare the ratios of their corresponding sides.
Let's calculate the ratios of the corresponding sides of Triangle I and Triangle II:
For Triangle I:
Side 1: 2 2/3 cm = 2 + 2/3 cm = 8/3 cm
Side 2: 4 1/2 cm = 4 + 1/2 cm = 9/2 cm
Side 3: 3 cm
For Triangle II:
Side 1: 8 cm
Side 2: 13 1/2 cm = 13 + 1/2 cm = 27/2 cm
Side 3: 9 cm
Now, let's find the ratios of the corresponding sides:
Ratio of Side 1: (8/3 cm) / (8 cm) = 1/3
Ratio of Side 2: (9/2 cm) / (27/2 cm) = 1/3
Ratio of Side 3: (3 cm) / (9 cm) = 1/3
Since the ratios of the corresponding sides of Triangle I and Triangle II are all equal to 1/3, we can conclude that the triangles are similar.
The ratio of correspondence between the sides is 1:3, meaning each side of Triangle I is one-third the length of the corresponding side in Triangle II.