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19) is incorrect. What about |dw:1440008761096:dw|
Is 19 the only one that is incorrect?
29) is incorrect. What about |dw:1440008841552:dw|
I believe 21 is correct.
Are they all wrong?
I believe 22 is correct. |dw:1440009068239:dw|
Sketch for 21. |dw:1440009258663:dw|
They are all B
Can you correct my work again?
Post a new queation and I'll be glad to have a look at it.
There is no requirement in the question that the quadrilateral be convex. In a polygon with 4 angles, angles that are not consecutive can be considered to be opposite.
Problem 20 states: two pairs of opposite angles are congruent You showed an example with a concave polygon with ONE pair of angles congruent. You have not shown a proper counterexample to dismiss the statement of problem 20.
In problem 20, the answer is "Suffucient".
Problem 19. Insufficient. Counterexample: an isosceles trapezoid. Problem 20. Sufficient. Problem 21. Insufficient. Counterexample: an isosceles trapezoid. Problem 22. Insufficient. Counterexample: a non-rhombus kite.
B A B B
So @mathstudent55 , I suppose you would also agree that the following quadrilateral is parallelogram? |dw:1440010612059:dw|
@ospreytriple In response to your last response: 1. These problems deal with convex polygons, so your figure is not illustrative of such a case. Even if you don't see any specific mention of it, we are dealing only with convex polygons. 2. More importantly, we are dealing with Problem 20. You even drew this figure (see below) when you were discussing problem 20. Problem 20 is about 2 pairs of opposite angles congruent, but your figure only shows one pair of congruent angles. That is why I said your figure was not a good counterexample for two pairs of opposite angles. |dw:1440036882588:dw| 3. With problem 19, about one pair of congruent angles, I definitely agree with you that that is insufficient info to prove the quadrilateral is a parallelogram.
@OM14forever Yes, that is correct. 19 B 20 A 21 B 22 B