Review Questions on Geometry 1: Where Did I Go Wrong?

[FredericChopin]

Hello,

I have been doing a review test on Geometry 1 on Sparknotes (http://www.sparknotes.com/math/geometry1/review/quiz.html), however I came across two questions which I got incorrect answers for and which I found the provided solutions questionable.

The first is Question 1 (attached).

I managed to find only 16 pairs of angles which were supplementary (attached is my solution), however this is not one of the solutions presented and the correct answer was that there were 36 pairs of supplementary angles.

The second is Question 2 (attached).

Simply attaching a triangle on a quadrilateral yields a pentagon, but in no way does it ever yield a quadrilateral, which was the correct solution to Question 2.

If you could suggest where I must have gone wrong, that would be appreciated.

Thank you.

 

[FredericChopin]

Also, have a look at this question (attached).

It's saying that the area of the parallelogram is 15 units squared. But that can't be right. The area of a parallelogram is its base multiplied by its altitude. That side which is labelled "5" clearly isn't an altitude.

 

[haruspex]

For q1, how many obtuse angles are there? How many acute angles are there?

For q2, the union can be a pentagon, as you say, but not necessarily. None of the offeed answers is correct.

For q3, I agree with you.

 

[ehild]

The second is Question 2 (attached).

Simply attaching a triangle on a quadrilateral yields a pentagon, but in no way does it ever yield a quadrilateral, which was the correct solution to Question 2.

If you could suggest where I must have gone wrong, that would be appreciated.

Thank you.

See the picture, what or those yellow shapes?

ehild

 

[haruspex]

See the picture, what or those yellow shapes?

ehild

View attachment 73987

I would not consider the second diagram an example of a quadrilateral and triangle sharing a side. But I do now see why D is correct. Consider two other sides crossing.

 

[FredericChopin]

These questions are dodgy, aren't they?

For q3, I agree with you.

Yeah. I think it is an error. They must have meant that the height of the parallelogram is 5, not one of its sides.

See the picture, what or those yellow shapes?

ehild

View attachment 73987

I would not consider the second diagram an example of a quadrilateral and triangle sharing a side. But I do now see why D is correct. Consider two other sides crossing.

The answer they provide is C, "quadrilateral". It seems that the resulting shape will be a polygon, but as ehild also showed, it could also be another quadrilateral, pentagon, or heptagon. Very dodgy.

I still don't understand how to answer Question 1. I still only see 16 pairs of supplementary angles, when the answer they provide is 36(!). Maybe they're trying to be picky and saying that, for example, "angle ABC" is not the same as "angle CBA". Hm...

 

[ehild]

Two angles are supplementary if their sum is 180°. You have 6 acute angles and 6 obtuse angles. How many acute-obtuse pairs can you make of them? a and 1 are supplementary, but so are a and 2 , a and 3 a and 4 and so on...

ehild

 

[haruspex]

The answer they provide is C, "quadrilateral". It seems that the resulting shape will be a polygon, but as ehild also showed, it could also be another quadrilateral, pentagon, or heptagon. Very dodgy.

Yes, it must always produce a polygon - what I meant to say is that it does not necessarily produce a convex polygon, nor even a polygon the sides of which correspond to the sides of the original shapes.

 

[ehild]

And a quadrilateral sharing two sides with a triangle can be a triangle :D

ehild