point O is on line segment NP. given OP = 10, NP = 2x, and NO = x + 7, determine the numerical length of NO.

Answer 1

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 \( \boxed{24} \).

Answer 2

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

Answer 3

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.