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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #302 : Right Triangles

Given: $\bigtriangleup ABC$ and $\bigtriangleup DEF$ .

$\angle B$ and $\angle E$ are both right angles.

$\overline{AB} \cong \overline{BC}$

$\overline{DE} \cong \overline{EF}$

True or false: From the given information, it follows that $\bigtriangleup ABC \cong \bigtriangleup DEF$ .

Possible Answers:

False

True

Correct answer:

False

Explanation:

The congruence of $\bigtriangleup ABC$ and $\bigtriangleup DEF$ cannot be proved from the given information alone. Examine the two triangles below:

Triangles 2

$\overline{AB} \cong \overline{BC}$ , $\overline{DE} \cong \overline{EF}$ , and $\angle B$ and $\angle E$ are both right angles, so the conditions of the problem are met; however, since the sides are not congruent between triangles - for example, $\overline{AB} \ncong \overline{DE}$ - the triangles are not congruent either.

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Example Question #1 : How To Find The Height Of A Right Triangle

A right triangle has a hypotenuse of 18 inches and a base of 12 inches. What is the height of the triangle in inches?

Possible Answers:

180.2

13.42

8.73

12.55

Correct answer:

13.42

Explanation:

We can find one leg of a right triangle when we have the length of the hypotenuse and the other leg. Square the hypotenuse and the known leg. Then, subtract the squared length of the leg from the squared length of the hypotenuse. Finally, find the square root of the result.

$\sqrt{18^{2}-12^{2}}=13.42$

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Example Question #1 : How To Find The Height Of A Right Triangle

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If c is not the base of the triangle, which of the following is the height?

Possible Answers:

None of the other answers

Correct answer:

Explanation:

If is not the base, that makes either or the base. If either or is the base, the right angle is on the bottom, so or respectively will be perpendicular. The height of a triangle is the distance from the base to the highest point, and in a right triangle that will be found by the side adjoining the base at a right angle. So if the base is , then and vise versa.

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Example Question #1 : How To Find The Height Of A Right Triangle

The area of a right triangle is 28. If one leg has a length of 7, what is the length of the other leg?

Possible Answers:

Correct answer:

Explanation:

We begin with the formula for the area of a triangle.

$A=\frac{1}{2}bh$

We further realize that the two legs of the triangle are the base and height; therefore, substituting what we know we get

$28=\frac{1}{2}(7)h$

$28=\frac{7}{2}h$

We can then solve by simply dividing.

8 = h

We have found our height and thus the second leg of our triangle.

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Example Question #1 : How To Find The Height Of A Right Triangle

If the area of a right triangle is , and the base of the right triangle is , what is the height of the right triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(16)}{4}=\frac{32}{4}=8$

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Example Question #1 : How To Find The Height Of A Right Triangle

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(10)}{5}=\frac{20}{5}=4$

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Example Question #1 : How To Find The Height Of A Right Triangle

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

1.5

4.5

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(15)}{10}=\frac{30}{10}=3$

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Example Question #3 : How To Find The Height Of A Right Triangle

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(24)}{4}=\frac{48}{4}=12$

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Example Question #4 : How To Find The Height Of A Right Triangle

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

4.5

13.5

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(45)}{10}=\frac{90}{10}=9$

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Example Question #1 : How To Find The Height Of A Right Triangle

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(20)}{1}=\frac{40}{1}=40$

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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #302 : Right Triangles

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #3 : How To Find The Height Of A Right Triangle

Example Question #4 : How To Find The Height Of A Right Triangle

Example Question #1 : How To Find The Height Of A Right Triangle

All Basic Geometry Resources

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