Triangle Height Verification: Analyzing a Perpendicular Line in Geometry

Triangle Altitudes with Perpendicular 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
00:00 Determine whether the straight line in the drawing is a height in the triangle
00:03 A height in a triangle extends from one of the triangle's vertices and is also perpendicular to the side
00:06 Therefore this line is the height, and that is the solution to the 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 straight line in the figure is the height of the triangle, we need to ensure it is a line that starts from a vertex of the triangle and is perpendicular to the opposite side, known as the base. In the context of geometry, this line is called an altitude.

According to the given figure, the straight line appears to stem from one vertex of the triangle and intersect the base at a right angle, as indicated by a small square or a perpendicular marker at their intersection.

Since the line in question meets the definition of an altitude (perpendicular from a vertex to the opposite side), it indeed represents the height of the triangle relative to that specific base.

Hence, the answer to the problem is Yes.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: Triangle height is a perpendicular line from vertex to opposite side
  • Recognition: Look for small square symbol showing 90° angle at intersection
  • Verification: Check that line starts at vertex and meets base perpendicularly ✓

Common Mistakes

Avoid these frequent errors
  • Confusing any line from vertex as height
    Don't assume every line from a vertex is the height = wrong identification! The line must be perpendicular to the opposite side, not just touch it. Always look for the right angle marker (small square) at the intersection point.

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

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

+

Look for the small square symbol at the intersection point! This symbol indicates a 90° angle, which means the line is perfectly perpendicular to the base.

Can a triangle have more than one height?

+

Yes! Every triangle has three different heights - one from each vertex to its opposite side. Each height corresponds to using a different side as the base.

What's the difference between height and altitude?

+

They're the same thing! Height and altitude both refer to the perpendicular distance from a vertex to the opposite side. Both terms are used interchangeably in geometry.

Does the height always fall inside the triangle?

+

Not always! In acute triangles, all heights fall inside. In obtuse triangles, two heights fall outside the triangle and must extend beyond the base to form the right angle.

Why is it important to identify the height correctly?

+

The height is crucial for calculating the triangle's area using the formula: Area=12×base×height Area = \frac{1}{2} \times base \times height . Using the wrong line gives incorrect area calculations!

🌟 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