Which of the following completes the proof?

triangles abc and edc are formed from segments bd and ac, in which point c is between points b and d and point e is between points a and c.

given: segment ac is perpendicular to segment bd

prove: δacb ~ δecd

reflect δecd over segment ac. this establishes that then, this establishes that ∠e'd'c' ≅ ∠abc. therefore, δacb ~ δecd by the aa similarity postulate.

∠abc ≅ ∠e'd'c'; translate point e' to point a
∠acb ≅ ∠e'c'd'; translate point e' to point b
∠acb ≅ ∠e'c'd'; translate point d' to point b
∠abc ≅ ∠e'd'c'; translate point d' to point a

Ageologist had two rocks on a scale that weighed 4.6 kilograms together. rock a was 0.5 of the total weight. how much did rock a weigh?

You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function. how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions

Drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. identify the domain for each of the given functions.