Question
The triangles shown are similar. Which side of triangle JGH corresponds to side PM of triangle PMO?
Triangle G H J. Side G H is 9 centimeters, H J is 12 centimeters, J G is 6 centimeters. Triangle P M O. Side P M is 3 centimeters, M O is 4.5 centimeters, O P is 6 centimeters.
GH
JG
HJ
OP
Triangle G H J. Side G H is 9 centimeters, H J is 12 centimeters, J G is 6 centimeters. Triangle P M O. Side P M is 3 centimeters, M O is 4.5 centimeters, O P is 6 centimeters.
GH
JG
HJ
OP
Answers
Answered by
GPT-4o mini
To identify which side of triangle JGH corresponds to side PM of triangle PMO, we have to look at the ratios of the corresponding sides of the similar triangles.
From triangle JGH:
- Side GH = 9 cm
- Side HJ = 12 cm
- Side JG = 6 cm
From triangle PMO:
- Side PM = 3 cm
- Side MO = 4.5 cm
- Side OP = 6 cm
Now, let's establish the ratios using the known side PM from triangle PMO:
1. The side PM of triangle PMO (3 cm) corresponds to the smallest side of triangle JGH (JG = 6 cm).
2. Triangle JGH and triangle PMO are similar, which means that the sides can be compared based on their proportional lengths.
Thus, side JG (6 cm) corresponds to side PM (3 cm).
Now let’s check the other sides for clarity:
- Side GH (9 cm) from triangle JGH could correspond to side OP (6 cm) of triangle PMO, since \(9 cm / 3 cm = 3\) (this maintains the ratio).
- Side HJ (12 cm) from triangle JGH corresponds to the longest side MO (4.5 cm) of triangle PMO, since \(12 cm / 4.5 cm = 2.67\).
So, the direct corresponding side for PM from triangle PMO is side JG from triangle JGH.
**The answer is: JG.**
From triangle JGH:
- Side GH = 9 cm
- Side HJ = 12 cm
- Side JG = 6 cm
From triangle PMO:
- Side PM = 3 cm
- Side MO = 4.5 cm
- Side OP = 6 cm
Now, let's establish the ratios using the known side PM from triangle PMO:
1. The side PM of triangle PMO (3 cm) corresponds to the smallest side of triangle JGH (JG = 6 cm).
2. Triangle JGH and triangle PMO are similar, which means that the sides can be compared based on their proportional lengths.
Thus, side JG (6 cm) corresponds to side PM (3 cm).
Now let’s check the other sides for clarity:
- Side GH (9 cm) from triangle JGH could correspond to side OP (6 cm) of triangle PMO, since \(9 cm / 3 cm = 3\) (this maintains the ratio).
- Side HJ (12 cm) from triangle JGH corresponds to the longest side MO (4.5 cm) of triangle PMO, since \(12 cm / 4.5 cm = 2.67\).
So, the direct corresponding side for PM from triangle PMO is side JG from triangle JGH.
**The answer is: JG.**