# SAT II Math II : Analyzing Figures

## Example Questions

### Example Question #1 : Analyzing Figures Refer to the above diagram. Which of the following is not a valid name for ?    All of the other choices give valid names for the angle. Explanation: is the correct choice. A single letter - the vertex - can be used for an angle if and only if that angle is the only one with that vertex. This is not the case here. The three-letter names in the other choices all follow the convention of the middle letter being vertex and each of the other two letters being points on a different side of the angle.

### Example Question #1 : Analyzing Figures Use the rules of triangles to solve for x and y.

x=45, y=45

x=30, y=30

x=60, y=30

x=30, y=60

x=60, y=30

Explanation:

Using the rules of triangles and lines we know that the degree of a straight line is 180. Knowing this we can find x by creating and solving the following equation:  Now using the fact that the interior angles of a triangle add to 180 we can create the following equation and solve for y:   ### Example Question #61 : Geometry Use the facts of circles to solve for x and y.

x=11, y= 39.5

x=10, y=30

x=13, y=10

x=39.5, y=11

x=11, y= 39.5

Explanation:

In this question we use the rule that oppisite angles are congruent and a line is 180 degrees. Knowing these two facts we can first solve for x then solve for y.  Then:     ### Example Question #71 : Geometry Solve for x and y using the rules of quadrilateral

x=6, y=10

x=9, y=6

x=6, y=9

x=2, y=4

x=6, y=9

Explanation:

By using the rules of quadrilaterals we know that oppisite sides are congruent on a rhombus. Therefore, we set up an equation to solve for x. Then we will use that number and substitute it in for x and solve for y.      ### Example Question #1 : Analyzing Figures

Chords and intersect at point  is twice as long as  and Give the length of .      Explanation:

If we let , then The figure referenced is below (not drawn to scale): If two chords intersect inside the circle, then the cut each other so that for each chord, the product of the lengths of the two parts is the same; in other words, Setting , and solving for :    Taking the positive square root of both sides: ,

the correct length of .

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