OpenStudy (anonymous):

Need help with 11 through 18 help anyone http://www.ocs.cnyric.org/webpages/jmelfi/files/GE09S3P1.PDF

4 years ago
OpenStudy (terenzreignz):

For number 14, you have a line AD which is parallel to BC, right, since it's a parallelogram?

4 years ago
OpenStudy (anonymous):

yes I got that

4 years ago
OpenStudy (terenzreignz):

The line AC is a transverse line to this set of parallel lines, so x and angle CAD, which measures 46 degrees, are congruent. Thus, x = 46 degrees.

4 years ago
OpenStudy (terenzreignz):

Because x and angle CAD are alternate interior angles.

4 years ago
OpenStudy (terenzreignz):

Then angle BCD measures 44 + 46 = 90 degrees, making it a right angle. This makes angle BAD a right angle as well. All quadrilaterals have interior angles that sum up to 360 degrees, and in parallelograms, opposite angles are congruent, so angle ABC is a right angle, as well as angle ADC. It's a rectangle.

4 years ago
OpenStudy (terenzreignz):

because all its interior angles are right angles. We know nothing about the lengths of the sides or the angle made by its diagonals, so we cannot say it's a square.

4 years ago
OpenStudy (anonymous):

Is it a rectangle then

4 years ago
OpenStudy (terenzreignz):

Yes, and that's the best we can say about it.

4 years ago
OpenStudy (anonymous):

okay so what would X be

4 years ago
OpenStudy (terenzreignz):

X is alternate interior to the angle measuring 46 degrees, and therefore has the same measure.

4 years ago
OpenStudy (anonymous):

oh ok so can we do number 11

4 years ago
OpenStudy (terenzreignz):

Right... For number 11, you can get the value of x immediately. Ever heard of vertical angles?

4 years ago
OpenStudy (anonymous):

yes isnt it V shape

4 years ago
OpenStudy (terenzreignz):

What's the vertical angle to the angle measuring x-degrees?

4 years ago
OpenStudy (terenzreignz):

Here's an example of a pair of vertical angles: |dw:1359433855891:dw|

4 years ago
OpenStudy (terenzreignz):

So clearly, x and the angle measuring 85 degrees are vertical angles. Vertical angles are always congruent, so x = 85 degrees.

4 years ago
OpenStudy (anonymous):

so the shape would be a square

4 years ago
OpenStudy (anonymous):

then you would subtract 180- 85 then get 95 to be y

4 years ago
OpenStudy (terenzreignz):

No. Remember that for something to be a square (or a rhombus, for that matter), the diagonals must be perpendicular. Are they?

4 years ago
OpenStudy (anonymous):

no

4 years ago
OpenStudy (anonymous):

would it be a parallelogram

4 years ago
OpenStudy (terenzreignz):

No. Let's take a piece of that square, shall we? |dw:1359434202358:dw|

4 years ago
OpenStudy (anonymous):

so it is a square

4 years ago
OpenStudy (terenzreignz):

|dw:1359434270176:dw| THIS is the angle that measures 95 degrees.

4 years ago
OpenStudy (terenzreignz):

They are ALL parallelograms.

4 years ago
OpenStudy (terenzreignz):

Again, for it to be a square, the diagonals MUST be perpendicular, and they're not, as you said.

4 years ago
OpenStudy (anonymous):

oh so I was right it is 95

4 years ago
OpenStudy (terenzreignz):

That angle is 95, but that is not y. In particular, since this is an isosceles triangle, then that other angle is also congruent to y |dw:1359434500655:dw|

4 years ago
OpenStudy (terenzreignz):

So, knowing that all triangles have interior angles summing up to 180, you get 95 + y + y = 180 2y = 85 y = 42.5

4 years ago
OpenStudy (anonymous):

oh ok

4 years ago
OpenStudy (terenzreignz):

Also, if you look at it, one of the angles of the parallelogram is right, but it is not a square, therefore, it must be a...?

4 years ago
OpenStudy (anonymous):

parallelogram

4 years ago
OpenStudy (anonymous):

no rectangle

4 years ago
OpenStudy (terenzreignz):

Yeah, it's a rectangle.

4 years ago
OpenStudy (anonymous):

okay and number 15

4 years ago
OpenStudy (terenzreignz):

All sides are congruent. It must at least be a...?

4 years ago
OpenStudy (anonymous):

rectangle

4 years ago
OpenStudy (terenzreignz):

Rhombus, it must least be a rhombus. Now, what we know about rhombuses, their diagonals bisect their interior angles... In particular, that 55 degrees is just half of that corner angle. Also, x is alternate interior to that 55-degree angle, so x is also 55 degrees. Now, we know one corner, as well as its opposite, measure twice 55, and that's 110 degrees apiece. Quadrilaterals have interior angles that measure 360 degrees, so y, as well as its opposite which also measures y degrees, so you get 110 + 110 + y + y = 360 2y + 220 = 360 2y = 140 y = 70

4 years ago
OpenStudy (terenzreignz):

Now, it's a rhombus, but the corners are not right angles, so it's not a square, it's just a rhombus.

4 years ago
OpenStudy (anonymous):

oh ok

4 years ago
OpenStudy (anonymous):

thank you so much i get it

4 years ago
OpenStudy (terenzreignz):

No problem Terence out :)

4 years ago
OpenStudy (anonymous):

ok

4 years ago