select all that applies

Answer:

A

C

D

F

G

Step-by-step explanation:

You can pretty easily find the answer by just going through each statement and analyzing what it means.  For A it asks if AB is parallel to DC (parallel means the lines could go on for infinity without ever touching) Looking at the shape we can see that AB and DC are on opposite sides and are slanted in the same direction meaning that they are in fact parallel.  This could be correct.  The next asks about angle BCD and whether or not it is congruent to CDA (congruent is just another word for the same) Angle BCD is the top right angle and we know this by following the letters on the shape in the order they were asked in the question.  We can see that these two angles are not congruent just via observation as BCD is an acute angle (less than 90 degrees with a right angle as a reference) and CDA is an obtuse angle (greater than 90 degrees)  This answer choice is incorrect.  Next up we have BPC and APD and it asks whether or not they are congruent.  We can apply the same logic to the previous choice and find out that they are in fact congruent angles which is also backed up by the rule of vertical angles which states that all vertical angles are congruent.  This means C is also a correct option.  Next up is line BC compared with AD which are very obviously congruent just by looking at the image, but we also know that opposite sides of a parallelogram are always congruent.  This answer choice is correct also.  Next up it asks us about AC in comparison to BD which are NOT congruent because each line has a different length due to the fact of the angles they are coming from.  AP is in fact congruent to PC because it is just a continual of the original line which stems from halfway across the middle of the parallelogram.  This IS a correct choice.  Next up it asks about supplementary angles and it is important to understand what that is before you can accurately answer the question.  Supplementary angles are angles which will total 180 degrees and the question specifically asks in relation to angles BAD and ADC.  These angles are in fact supplementary because they are across from each other at the base of the parallelogram and we know from theories that these angles will always be supplementary in these shapes.  G is also a correct answer.  Last but not least we have a question asking us about APB and APD and whether or not they are vertical angles.  Vertical angles are angles which are across from each other either vertically as the name sake says or horizontally, but they have to be directly across from each other.  Looking at the image we can clearly see that these angles are NOT across from each other but instead are adjacent to each other (next to each other) meaning the last option is not correct.  This leaves A,C,D,F, and G as the correct answers.

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