### All ISEE Lower Level Math Resources

## Example Questions

### Example Question #51 : How To Find The Perimeter Of A Triangle

Find the length of one side of an equilateral triangle that has a perimeter of 27cm.

**Possible Answers:**

**Correct answer:**

The formula to find perimeter of an equilateral triangle is

where *a* is the length of one side. We can multiply that by 3, because an equilateral triangle has 3 equal sides. Now, to find the length of one side, we will solve for *a*.

So, we know the perimeter of the equilateral triangle is 27cm. Knowing this, we can substitute. We get

Therefore, the length of one side of the equilateral triangle is 9cm.

### Example Question #1321 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Use the following triangle to answer the question:

Find the perimeter.

**Possible Answers:**

**Correct answer:**

To find the perimeter of a triangle, we will use the following formula:

where *a, b, *and *c* are the lengths of the sides of the triangle.

Now, given the triangle

we can see that it has sides of length 8ft, 4ft, and 7ft. So, we get

### Example Question #1 : How To Find Symmetry

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?

**Possible Answers:**

Trapezoid

Quadrilateral

None of these

Rectangle

Parallelogram

**Correct answer:**

Quadrilateral

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?

**Possible Answers:**

**Correct answer:**

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 #2 : How To Find Symmetry

How many lines of symmetry are there in a square?

**Possible Answers:**

**Correct answer:**

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 #1 : Lines

What is the distance between and ?

**Possible Answers:**

**Correct answer:**

The distance formula is .

Let and :

### Example Question #372 : Plane Geometry

What is the distance between and ?

**Possible Answers:**

**Correct answer:**

The distance formula is given by .

Let and :

### Example Question #1 : How To Find Length Of A Line

What is the distance between and ?

**Possible Answers:**

**Correct answer:**

The distance formula is given by .

Let and :

### Example Question #1 : How To Find Length Of A Line

What is the distance between the points and ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 .

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