# ISEE Lower Level Math : Lines

## Example Questions

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### Example Question #374 : Plane Geometry

There is a four sided figure in which none of the lines run parallel to each other. Which of the following could be the appropriate term to describe the figure?

Rectangle

None of these

Trapezoid

Parallelogram

Explanation:

A key characteristic of a rectangle, parallelogram, and trapezoid is the fact that they each have at least one pair of lines that run parallel to each other. The only option that has lines that may not run parallel to each other is the quadrilateral, which must simply have four sides but has no specifications about parallelism.

### Example Question #1 : Lines

If a diagonal is drawn from one corner of a rectangle to the opposite corner, what 2 shapes result?

Explanation:

While drawing a line across a rectangle (so that it bisects 2 sides) can result in 2 quadrilaterals, squares, or rectangles, a line drawn from one corner to the furthest corner results in two triangles. Therefore, the correct answer choice is 2 triangles.

### Example Question #376 : Plane Geometry

How many lines of symmetry are there in a square?

Explanation:

A line of symmetry is a line that divides a polygon in half and each half is a mirror image of the other. In other words, you can fold the polygon over the symmetry line and each half matches up perfectly.

For a square there are four lines of symmetry. Two are from the diagonals of the square and two are from connecting the midpoints of the opposite sides.

### Example Question #1324 : Isee Lower Level (Grades 5 6) Mathematics Achievement

What is the distance between and ?

Explanation:

The distance formula is .

Let  and :

### Example Question #378 : Plane Geometry

What is the distance between and ?

Explanation:

The distance formula is given by .

Let and :

### Example Question #379 : Plane Geometry

What is the distance between and ?

Explanation:

The distance formula is given by .

Let  and :

### Example Question #380 : Plane Geometry

What is the distance between the points and ?

Explanation:

The distance formula is .

Let and .

Plug these two points into the distance formula:

### Example Question #1 : Lines

If a line with a length of 5 starts at the point , which of the following is NOT a possible end point?

Explanation:

Let , and let be the end point we are looking for.

Recall the distance formula:

Squaring the distance formula gives .

Plug this squared distance formula and solve for :

Substitute each response into this equation to see which one is false.  The only response that doesn't work is .

### Example Question #401 : Geometry

What is the distance between and ?

Explanation:

The distance formula is .

Let and .

Plug these points into the distance formula:

### Example Question #402 : Geometry

If a line that is 13 inches in length starts at the point , which of the following is NOT a possible end point?

Explanation:

The distance formula is given by .

Square both sides:

Now, let , and let be the end point we are looking for.

Plug into the squared distance formula and solve for :

Alternatively, you can plug in the answer choices and see which point makes the above equation untrue.  The point matches this description and is therefore the correct answer.

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