I'm studying for my act and I have no clue how to do geometry. Please can help and show me steps in how to work these two problems? I have no idea how to get the answers. In the first one all the...

I'm studying for my act and I have no clue how to do geometry. Please can help and show me steps in how to work these two problems? I have no idea how to get the answers. In the first one all the study guide tells me about it is. Since uy and vx are line segments angles UWV and XWY are vertical angles.therefore you can conclude that C°=d°. I have know idea what it's talking about. And on the second one it just tells me what I should and shouldn't assume. I'm so confused and lost. 

Asked on by hexgirl21

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

You have not provided all the information required to give you a satisfactory answer. This makes it quite difficult to do the same.

In the first question, the information provided seems to suggest two line segments UY and VX that intersect at point W.

Vertical angles refer to a pair of non-adjacent angles formed when two straight lines intersect. `/_UWV` and `/_XWY` are vertical angles. The angles `/_UWY` and `/_VWX` are equal to 180 degrees as they are formed by three points lying along on a straight line.

Now `/_ UWV + /_UWX = 180^@` , `/_UWX + /_XWY = 180^@` .

From the two equations we get:

`/_ UWV + /_UWX = /_UWX + /_XWY = 180^@`

`/_ UWV = /_XWY`

This proves that vertical angles are equal.

The angles `/_C` and `/_D` that you have mentioned refer to either `/_UWV ` and `/_XWY` or to `/_UWX` and `/_VWY` .

This allows us to conclude that `/_C = /_D`

As for your second question, when a diagram is given there are some assumptions that can be made and some that cannot. For example, given the intersection of two lines, the angle at which they intersect could look like it is a right angle, but if the exact value is not provided assuming the same may give an incorrect answer. Similarly, it may not be true that two lines are parallel though they may appear to be parallel in the diagram. It is therefore important to know what you can assume and what you shouldn't assume to arrive at the correct answer.

mr-mayonnaise's profile pic

mr-mayonnaise | Middle School Teacher | (Level 1) Assistant Educator

Posted on

Hello, your data you have given us makes very little sense without a picture. I'm going to create one and attach it to the picture. Use it as reference to the following explanation. 

line segment is a line with two end points. In this case your two line segments should be UY and XV with both having a point W at the intersection of the two segments. 

Angle UWV refers to the angle created by following the lines from point U to point W then to point Y. This makes an angle of some size which we will call Angle C. Angle XWY refers to the angle on the other side of the graph and I will call it Angle D.

Vertical Angles are two angles that are across each other on an intersection of two line segments or lines. Vertical opposite angels are always equal to one another. The reasoning (and proof) is below (if you don't follow, just remember than angles across an intersection are vertical opposite and thus equal):

Using this knowledge of vertical angles you should be able to give the simple reasoning that vertical opposite angles are always equal. This applies as well to the other two angles shown, my UWX and VWY. These are opposite and 'vertical' and thus equal to one another as well. 

Proof is as follows:

`/_UWY = 180@`

`/_UWY = /_UWV + /_VWY`

`:. /_UWV + /_VWY = 180@`

Using this we prove that those two angels add to make 180 degrees. If we move to the other side but still share the angle VWY...

`/_XWV = 180@`

`/_XWY + /_VWY = /_ XWV`

`:. /_ XWY + /_VWY = 180@`

So we have found the same relationship on the other side.

But if put these equations across from one another...

 `/_UWV + /_ VWY = 180@ = /_ XWY + VWY`

`OR... /_UWV + /_VWY = /_XWY + /_VWY`

Subtract like terms:

`/_UWV +(/_VWY - /_VWY) = /_XWY + (/_VWY - /_VWY)`

`:. /_UWV = /_XWY`

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