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 parallel to side dc so the alternate interior angles, angle abd and angle cdb, are congruent. side ab is equal to side dc and db is the side common to triangles abd and bcd. therefore, the triangles abd and bcd 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 which are congruent form a pair of vertical angles which are congruent

To prove ABCD is a parallelogram, the phrase that completes the proof is "Angle DBC and angle ADB form a pair of alternate interior angles which are congruent"

Step-by-step explanation:

In a parallelogram, opposite sides are equal and parallel.

AB || DC and AB=DC as given. We only need to show AD || BC and AD=BC So, by congruency properties AD=BC is shown. And for showing AD || BC pair of alternate interior angles should be equal.

Hence, Phrase C : 'Angle DBC and angle ADB form a pair of alternate interior angles which are congruent' completes the proof.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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