Angle2 = angle their corresponding angles of parallel lines cut by traversal

angle 5= angle by the vertical angles theorem

Angle2 = angle _6__because their corresponding angles of parallel lines cut by traversal

Angle 5 =angle 8 by vertical angle theorem.

Step-by-step explanation:

Corresponding angles:

If two lines are parallel and a transversal intersect at two points of the parallel lines then we have corresponding angles are equal.

In the figure the corresponding pair angles given below are equal :

angle 2 and angle 6

angle 4 and angle 8

angle 1 and angle 5

angle 3 and angle 7

Vertical angle theorem:

If two lines intersect each other then vertical opposite angles are equal.

In the figure the pair of vertical angles which are equal are

angle 2 and angle 3

angle 1 and angle 4

angle 5 and angle 8

angle 6 and angle 7

Angle2 = angle _6__because their corresponding angles of parallel lines cut by traversal

Angle 5 =angle 8 by vertical angle theorem.

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.