Triangle Height Verification: Is the Given Line an Altitude?

Triangle Altitudes with Line Orientation

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's find out if the straight line in the drawing is a height of the triangle.
00:08 Remember, a height starts at a corner of the triangle. It must also be perpendicular to the opposite side.
00:15 By sketching possible heights, we see that none match these rules.
00:19 So, the line isn't a height. And that's the answer!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

2

Step-by-step solution

To determine if the given line in the triangle is the height, we need to check if it satisfies the conditions of a triangle's altitude.

  • Step 1: Identify the base of the triangle. The problem suggests that the horizontal line, presumably at the bottom of the triangle, acts as the base.
  • Step 2: The altitude must be drawn from the vertex opposite to the base and be perpendicular to this base. Thus, the potential altitude would start at the apex of the triangle.
  • Step 3: The given figure features a straight line connecting two points on the interior of the triangle and is not perpendicular to the base.

Therefore, this line cannot be the height because it does not extend perpendicularly from the apex opposite the base to the base itself.

Thus, the correct answer is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Definition: An altitude must be perpendicular to the base
  • Technique: Check if line connects vertex to opposite side at 90°
  • Check: Verify line starts from vertex and hits base perpendicularly ✓

Common Mistakes

Avoid these frequent errors
  • Assuming any line from vertex to base is an altitude
    Don't think every line from a vertex to the opposite side is an altitude = wrong identification! The line must form a 90° angle with the base. Always check if the line is perpendicular to the base it intersects.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

What exactly makes a line an altitude in a triangle?

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An altitude must satisfy two conditions: it starts from a vertex and is perpendicular to the opposite side (base). Just connecting vertex to base isn't enough!

How can I tell if a line is perpendicular to the base?

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Look for a 90° angle marker (small square) where the line meets the base. If there's no right angle marker, the line is likely not perpendicular.

Can a triangle have more than one altitude?

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Yes! Every triangle has exactly three altitudes - one from each vertex to its opposite side. They all meet at a point called the orthocenter.

What if the line doesn't start from a vertex?

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Then it's definitely not an altitude! An altitude must always start from one of the three vertices of the triangle and extend to the opposite side.

Does the altitude always fall inside the triangle?

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Not always! In obtuse triangles, some altitudes fall outside the triangle. But they still must be perpendicular to the extended base line.

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