Kelly and daniel wrote the following proofs to prove that vertical angles are congruent. who is correct? line segment nt intersects line segment mr forming four angles. angles 1 and 3 are vertical angles. angles 2 and 4 are vertical angles. kelly's proof statement justification ∠2 = ∠4 vertical angles are congruent. ∠1 = ∠3 vertical angles are congruent. vertical angles are congruent. vertical angle theorem daniel's proof statement justification ∠1 + ∠2 = 180° definition of supplementary angles ∠1 + ∠4 = 180° definition of supplementary angles ∠1 + ∠2 = ∠1 + ∠4 transitive property of equality ∠2 = ∠4 subtraction property of equality both kelly and daniel are correct. neither kelly or daniel is correct. kelly is correct, but daniel is not. daniel is correct, but kelly is not.

The answer is Daniel is correct, but Kelly is not.

Step-by-step explanation:

(D) Daniel is correct, but Kelly is not.

Step-by-step explanation:

It is given that Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles.

Kelly's Proof:∠2 = ∠4 (Vertical angles are congruent)

∠1 = ∠3(Vertical angles are congruent)

Using Vertical Angle Theorem  the vertical angles are equal.

since, we cannot use the direct information given in the question in order to prove the same.

Thus, the justification given by Kelly is incorrect.

Now, Daniel's proof:

∠1 + ∠2 = 180°(Definition of Supplementary Angles)

and ∠1 + ∠4 = 180° (Definition of Supplementary Angles)

⇒∠1 + ∠2 = ∠1 + ∠4(Transitive Property of Equality)

Hence,  ∠2 = ∠4(Subtraction Property of Equality)

Thus, the justification of Daniel is correct.

Hence, option (D) is correct.

she will travel a distance in the range of 3 - 11 miles

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.