△GHJ∼△MNP
Which statements are true?
Select each correct answer.
m∠J=m∠P (TRUE)
∠H≅∠N (TRUE)
HJ¯≅NP¯ (it has the line over them) false
GH=MN (TRUE)
GJ/MP=GH/MN ( TRUE )
Looks good, but:
why do you think GH=MN?
and are not these also line segments, as in the previous question?
The correct answers are:
1. m∠J = m∠P (TRUE)
2. ∠H ≅ ∠N (TRUE)
3. HJ ¯≅ NP ¯ (FALSE)
4. GH = MN (TRUE)
5. GJ/MP = GH/MN (TRUE)
To determine which statements are true for the given similar triangles ∆GHJ ∼ ∆MNP, we can use the properties of similar triangles. Here's how:
1. m∠J = m∠P (TRUE):
Corresponding angles in similar triangles are equal, so this statement is true.
2. ∠H ≅ ∠N (TRUE):
Since ∆GHJ ∼ ∆MNP, the corresponding angles H and N are equal. Therefore, this statement is true.
3. HJ¯ ≅ NP¯ (FALSE):
For corresponding sides in similar triangles, you cannot conclude that they are equal unless you have additional information. Therefore, this statement is false.
4. GH = MN (TRUE):
Corresponding sides in similar triangles are proportional. Since ∆GHJ ∼ ∆MNP, the ratio of corresponding sides is equal. Therefore, this statement is true.
5. GJ/MP = GH/MN (TRUE):
In similar triangles, the corresponding sides are proportional. Therefore, GJ/MP is equal to GH/MN. Thus, this statement is true.
Therefore, the true statements are:
m∠J = m∠P
∠H ≅ ∠N
GH = MN
GJ/MP = GH/MN