Question
point O is on line segment NP. given OP = 10, NP = 2x, and NO = x + 7, determine the numerical length of NO.
Answers
GPT-4o mini
To find the numerical length of NO, we first note that since point O is on line segment NP, we can express the relationship between the segments using the provided information:
1. \( NP = NO + OP \)
By substituting the given values into this equation, we have:
\[
2x = NO + 10
\]
We are also given that:
\[
NO = x + 7
\]
Now, we can substitute \( NO \) in the equation for \( NP \):
\[
2x = (x + 7) + 10
\]
\[
2x = x + 17
\]
Now, subtract \( x \) from both sides:
\[
2x - x = 17
\]
\[
x = 17
\]
Now that we have the value of \( x \), we can substitute it back into the equation for \( NO \):
\[
NO = x + 7
\]
\[
NO = 17 + 7
\]
\[
NO = 24
\]
Thus, the numerical length of \( NO \) is \( \boxed{24} \).
1. \( NP = NO + OP \)
By substituting the given values into this equation, we have:
\[
2x = NO + 10
\]
We are also given that:
\[
NO = x + 7
\]
Now, we can substitute \( NO \) in the equation for \( NP \):
\[
2x = (x + 7) + 10
\]
\[
2x = x + 17
\]
Now, subtract \( x \) from both sides:
\[
2x - x = 17
\]
\[
x = 17
\]
Now that we have the value of \( x \), we can substitute it back into the equation for \( NO \):
\[
NO = x + 7
\]
\[
NO = 17 + 7
\]
\[
NO = 24
\]
Thus, the numerical length of \( NO \) is \( \boxed{24} \).
Step Statement Reason
1
triangle, A, D, B, \cong, triangle, B, C, A△ADB≅△BCA
Given
2
angle, D, \cong, angle, C∠D≅∠C
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
3
start overline, D, A, end overline, \cong, start overline, C, B, end overline
DA
≅
CB
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
4
angle, D, E, A, \cong, angle, C, E, B∠DEA≅∠CEB
Vertical angles are congruent
5
6
start overline, D, E, end overline, \cong, start overline, C, E, end overline
DE
≅
CE
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
what should u say on 5
1
triangle, A, D, B, \cong, triangle, B, C, A△ADB≅△BCA
Given
2
angle, D, \cong, angle, C∠D≅∠C
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
3
start overline, D, A, end overline, \cong, start overline, C, B, end overline
DA
≅
CB
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
4
angle, D, E, A, \cong, angle, C, E, B∠DEA≅∠CEB
Vertical angles are congruent
5
6
start overline, D, E, end overline, \cong, start overline, C, E, end overline
DE
≅
CE
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
what should u say on 5
GPT-4o mini
For step 5, it appears that you are trying to establish a relationship that justifies the congruence of line segments \(DE\) and \(CE\). To do this, you can state one of the following:
**Option 1: If the triangles \( \triangle ADB \) and \( \triangle BCA \) are congruent, then the corresponding sides \( DE \) and \( CE \) must also be congruent.**
You could phrase step 5 as follows:
**5. Triangle \( \triangle ADB \cong \triangle BCA \)**
**Reason:** Corresponding parts of congruent triangles are congruent (CPCTC).
This directly supports the conclusion that \( DE \cong CE \) which is stated in step 6.
**Option 1: If the triangles \( \triangle ADB \) and \( \triangle BCA \) are congruent, then the corresponding sides \( DE \) and \( CE \) must also be congruent.**
You could phrase step 5 as follows:
**5. Triangle \( \triangle ADB \cong \triangle BCA \)**
**Reason:** Corresponding parts of congruent triangles are congruent (CPCTC).
This directly supports the conclusion that \( DE \cong CE \) which is stated in step 6.