Examples with solutions for Parts of a Triangle: Identifying and defining elements

Exercise #1

Given the following triangle:

Write down the height of the triangle ABC.

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Video Solution

Step-by-Step Solution

An altitude in a triangle is the segment that connects the vertex and the opposite side, in such a way that the segment forms a 90-degree angle with the side.

If we look at the image it is clear that the above theorem is true for the line AE. AE not only connects the A vertex with the opposite side. It also crosses BC forming a 90-degree angle. Undoubtedly making AE the altitude.

Answer

AE

Exercise #2

Which of the following is the height in triangle ABC?

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Video Solution

Step-by-Step Solution

Let's remember the definition of height of a triangle:

A height is a straight line that descends from the vertex of a triangle and forms a 90-degree angle with the opposite side.

The sides that form a 90-degree angle are sides AB and BC. Therefore, the height is AB.

Answer

AB

Exercise #3

Can a triangle have two right angles?

Video Solution

Step-by-Step Solution

The sum of angles in a triangle is 180 degrees. Since two angles of 90 degrees equal 180, a triangle can never have two right angles.

Answer

No

Exercise #4

Look at the two triangles below. Is EC a side of one of the triangles?

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Video Solution

Step-by-Step Solution

Every triangle has 3 sides, let's go over the triangle on the left side:

Its sides are: AB, BC, CA

This means that in this triangle, side EC does not exist.

Let's go over the triangle on the right side:

Its sides are: ED, EF, FD

This means that in this triangle, side EC does not exist.

Therefore, EC is not a side in either of the triangles.

Answer

No.

Exercise #5

True or false:

DE not a side in any of the triangles.
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Video Solution

Answer

True

Exercise #6

Is DE side in one of the triangles?
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Video Solution

Answer

Not true

Exercise #7

Given the following triangle:

Write down the height of the triangle ABC.

AAABBBCCCDDD

Video Solution

Answer

AD

Exercise #8

Given the following triangle:

Write down the height of the triangle ABC.

AAABBBCCCDDD

Video Solution

Answer

BD

Exercise #9

Given the following triangle:

Write down the height of the triangle ABC.

AAABBBCCCDDD

Video Solution

Answer

AD

Exercise #10

Given the following triangle:

Write down the height of the triangle ABC.

AAABBBCCCDDD

Video Solution

Answer

BD

Exercise #11

Determine the type of angle given.

Video Solution

Answer

Map

Exercise #12

Determine the type of angle given.

Video Solution

Answer

Straight

Exercise #13

Determine the type of angle given.

Video Solution

Answer

Acute

Exercise #14

Determine the type of angle given.

Video Solution

Answer

Obtuse

Exercise #15

Is the straight line in the figure the height of the triangle?

Video Solution

Answer

No

Exercise #16

Is the straight line in the figure the height of the triangle?

Video Solution

Answer

No

Exercise #17

Is the straight line in the figure the height of the triangle?

Video Solution

Answer

Yes

Exercise #18

Is the straight line in the figure the height of the triangle?

Video Solution

Answer

Yes

Exercise #19

Is the straight line in the figure the height of the triangle?

Video Solution

Answer

Yes

Exercise #20

Is the straight line in the figure the height of the triangle?

Video Solution

Answer

No