If angle A is congruent to itself by the Reflexive Property, which transformation could be used to prove ΔABC ~ ΔADE by AA similarity postulate? triangles ABC and ADE, in which point D is between points A and B and point E is between points A and C

Translate triangle ADE so that point D lies on point B to confirm ∠D ≅ ∠B.
Translate triangle ADE so that point B lies on point E to confirm ∠B ≅ ∠E.
Dilate ΔABC from point A by the ratio segment AD over segment AB to confirm segment AD ~ segment AB.
Dilate ΔABC from point A by the ratio segment AE over segment AC to confirm segment AE ~ segment AC.

the answer is 13 cm

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.