The figure below shows a quadrilateral ABCD. Sides AB and DC are equal and parallel: A quadrilateral ABCD is shown with the opposite sides AB and DC shown parallel and equal.

A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram:

Side AB is equal to side DC, and DB is the side common to triangles ABD and CDB. Angle ABD is congruent to angle CDB by Alternate Interior Angles. Therefore, the triangles ABD and CDB are congruent by SAS postulate. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB . Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Which phrase best completes the student's proof?

are congruent by the AAS postulate
are congruent by the ASA postulate
form a pair of alternate interior angles that are congruent
form a pair of vertical angles that are congruent

Which expression is equivalent to 3^3 + 2^2?

The probability that a student graduating from suburban state university has student loans to pay off after graduation is .60. if two students are randomly selected from this university, what is the probability that neither of them has student loans to pay off after graduation?

Listed below are time intervals (min) between eruptions of a geyser. assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. do not assume that the population standard deviations are equal. does it appear that the mean time interval has changed? is the conclusion affected by whether the significance level is 0.10 or 0.01? recent 78 90 90 79 57 101 62 87 71 87 81 84 57 80 74 103 62 past 88 89 93 94 65 85 85 92 87 91 89 91 follow the steps of hypothesis testing, including identifying the alternative and null hypothesis, calculating the test statistic, finding the p-value, and making a conclusions about the null hypothesis and a final conclusion that addresses the original claim. use a significance level of 0.10. is the conclusion affected by whether the significance level is 0.10 or 0.01? answer choices below: a) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.01 but is not rejected when the significance level is 0.10. b) no, the conclusion is not affected by the significance level because h0 is not rejected regardless of whether a significance level of 0.10 or 0.01 is used. c) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.10 but is not rejected when the significance level is 0.01. d) no, the conclusion is not affected by the significance level because h0 is rejected regardless of whether a significance level of 0.10 or 0.01 is used.