Triangle Height Verification: Analyzing a Geometric Construction

Triangle Heights with Perpendicular Line Verification

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

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's find out if the line in the drawing is a height in the triangle.
00:08 A height starts from one vertex, and goes straight down to meet the opposite side at a right angle.
00:14 This line doesn't start from a vertex, and it's not perpendicular to the side.
00:19 So, this line isn't a height. And that's how we solve this question!

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 straight line is the height of the triangle, we need to check whether it is perpendicular to the side it intersects (or its extension), which is the definition of a height (altitude) in a triangle.

Looking at the figure, the straight line is drawn from a vertex of the triangle to a point on the opposite side, but it is not perpendicular to that side or its extension. Therefore, the line does not meet the criteria for being a height of the triangle.

In conclusion, the line is not the height of the triangle because it is not perpendicular to the opposite side.

Therefore, the correct answer to the problem is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Definition: Triangle height must be perpendicular to opposite side
  • Technique: Check for 90° angle between line and base
  • Check: Verify perpendicular symbol or right angle marking in figure ✓

Common Mistakes

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

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 the height of a triangle?

+

A triangle's height (or altitude) is a line segment from any vertex that is perpendicular to the opposite side (or its extension). The key word is perpendicular - it must form a 90° angle!

How can I tell if a line is perpendicular in a diagram?

+

Look for these clues: a small square symbol at the intersection point, a right angle marking, or lines that clearly form 90° angles. If you don't see these indicators, the line likely isn't perpendicular.

Can a triangle have more than one height?

+

Yes! Every triangle has exactly three heights - one from each vertex to the opposite side. Each height is perpendicular to its corresponding base.

What if the height falls outside the triangle?

+

That's normal for obtuse triangles! The height extends to the extension of the opposite side, not the side itself. It's still perpendicular and still counts as a valid height.

Does the height always go to the middle of the opposite side?

+

No! The height goes to wherever it can be perpendicular to the opposite side. This might be at the middle, near an end, or even on an extension of the side.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Triangle questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations