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ISEE Lower Level Math : Geometry

Study concepts, example questions & explanations for ISEE Lower Level Math

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All ISEE Lower Level Math Resources

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Example Questions

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Example Question #53 : How To Find The Perimeter Of A Triangle

Use the following triangle to answer the question:

Triangle5

Find the perimeter.

Possible Answers:

$16\text{ft}$

$20\text{ft}$

$17\text{ft}$

$19\text{ft}$

$18\text{ft}$

Correct answer:

$19\text{ft}$

Explanation:

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

P = a+b+c

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

Now, given the triangle

Triangle5

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

$P = 8\text{ft} + 4\text{ft} + 7\text{ft}$

$P = 19\text{ft}$

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Example Question #54 : How To Find The Perimeter Of A Triangle

An equilateral triangle has a perimeter of 42 cm. What is the length of one of its sides?

Possible Answers:

$12\ cm$

$16\ cm$

$14\ cm$

$20\ cm$

$10\ cm$

Correct answer:

$14\ cm$

Explanation:

By definition, an equilateral triangle is a triangle with three equal sides. That is, the length of each side of the triangle is going to be the same.

In this problem, we know that the perimeter (the sum of all the lengths) is 42 cm.

Side 1 + Side 2 + Side 3 = 42 cm.

Since the sides are equal, we can write the following equation. S = one side of the triangle

3S=42 cm.

To find the length of one side of the triangle, we would then divide 3 from both sides.

$\frac{3}{3}S=\frac{42}{3}$

1S=14 Remember that 1*S is the same as

$S=14\ cm.$

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Example Question #1 : Lines

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:

Quadrilateral

Trapezoid

None of these

Rectangle

Parallelogram

Correct answer:

Quadrilateral

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.

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Example Question #392 : Geometry

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

Possible Answers:

$2\ \textup{quadrilaterals}$

$2\ \textup{triangles}$

$2\ \textup{squares}$

$2\ \textup{rectangles}$

Correct answer:

$2\ \textup{triangles}$

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.

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Example Question #393 : Geometry

How many lines of symmetry are there in a square?

Possible Answers:

Correct answer:

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.

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

What is the distance between (2,5) and (-7, 17) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is $d=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$ .

Let $P_{1}=(-7,17)$ and $P_{2}=(2,5)$ :

$d=\sqrt{(2-(-7))^{2} + (5-17)^{2}}=\sqrt{(9)^{2} + (-12)^{2}}=\sqrt{81 + 144}=\sqrt{225}=15$

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Example Question #2 : How To Find Length Of A Line

What is the distance between (-2, 3) and (4, -5) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is given by $d=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$ .

Let $P_{1}=(4,-5)$ and $P_{2}=(-2,3)$ :

$d=\sqrt{(-2-4)^{2} + (3-(-5)^{2}}=\sqrt{(-6)^{2} + (8)^{2}}=\sqrt{36 + 64}=\sqrt{100}=10$

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Example Question #1331 : Isee Lower Level (Grades 5 6) Mathematics Achievement

What is the distance between (1,-3) and (13,-8) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is given by $d=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$ .

Let $P_{1}=(1,-3)$ and $P_{2}=(13,-8)$ :

$d=\sqrt{(13-1)^{2} + (-8-(-3)^{2}}=\sqrt{(12)^{2} + (-5)^{2}}=\sqrt{144 + 25}=\sqrt{169}=13$

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

What is the distance between the points (-2,1) and (10,-4) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is $d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ .

Let $P_{1}= (-2, 1)$ and $P_{2}=(10, -4)$ .

Plug these two points into the distance formula:

$d = \sqrt{(10-(-2))^{2}+(-4-1)^{2}}=\sqrt{(12)^{2}+(-5)^{2}}=\sqrt{144+25}=\sqrt{169}=13$

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Example Question #5 : How To Find Length Of A Line

If a line with a length of 5 starts at the point (1,1) , which of the following is NOT a possible end point?

Possible Answers:

(5, -2)

(4, 5)

(-3, 4)

(-2, -3)

(-3,5)

Correct answer:

(-3,5)

Explanation:

Let $P_{1}=(1,1)$ , and let $P_{2}$ be the end point we are looking for.

Recall the distance formula:

$d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Squaring the distance formula gives $d^{2} = (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$ .

Plug $P_{1}=(1,1)$ this squared distance formula and solve for $P_{2}$ :

$25 = (x_{2}-1)^{2}+(y_{2}-1)^{2}$

Substitute each response into this equation to see which one is false. The only response that doesn't work is (-3, 5) .

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ISEE Lower Level Math : Geometry

Study concepts, example questions & explanations for ISEE Lower Level Math

All ISEE Lower Level Math Resources

Example Questions

Example Question #53 : How To Find The Perimeter Of A Triangle

Example Question #54 : How To Find The Perimeter Of A Triangle

Example Question #1 : Lines

Example Question #392 : Geometry

Example Question #393 : Geometry

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

Example Question #2 : How To Find Length Of A Line

Example Question #1331 : Isee Lower Level (Grades 5 6) Mathematics Achievement

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

Example Question #5 : How To Find Length Of A Line

All ISEE Lower Level Math Resources

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