Geometric Analysis: Identifying the Correct Height of a Triangle

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

Look for a right angle symbol (small square) where the line meets the base. In diagrams, this symbol indicates a 90° angle, confirming the line is the height.

Q: Can a triangle have more than one height?

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

Q: Does the height always fall inside the triangle?

Not always! In obtuse triangles, some heights fall outside the triangle. The height line extends beyond the triangle to meet the extended base line perpendicularly.

Q: Why is knowing the height important?

Triangle height is essential for calculating area using the formula: $ Area = \frac{1}{2} \times base \times height $. Without the correct height, your area calculation will be wrong!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether the straight line in the drawing a height in the triangle

00:02 A height in a triangle extends from one of the triangle's vertices and is also perpendicular to the side

00:05 Therefore this line is the height, and this 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

The task is to determine whether the line shown in the diagram serves as the height of the triangle. For a line to be considered the height (or altitude) of a triangle, it needs to be a perpendicular segment from a vertex to the line that contains the opposite side, often referred to as the base.

Let's analyze the diagram:

The triangle is described by its vertices, forming a shape, and one side is the base. There's a line drawn from one vertex directed toward the opposite side.
To be the height, this line must be perpendicular to the side it meets (the base).
Though the figure does not explicitly show perpendicularity with a right angle mark, the line appears as a straight, direct connection from the vertex to the base. This is typically indicative of it being a height.
Assuming typical geometric conventions and the common depiction of heights in diagrams, the line shows properties consistent with being perpendicular to the opposite side, thereby functioning as the height.

Based on the analysis, the line is indeed the height of the triangle. Thus, the answer is Yes.

Therefore, the solution to the problem is Yes.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Height is perpendicular segment from vertex to opposite side
Technique: Look for right angle symbol or perpendicular indicator at base
Check: Verify line forms 90° angle with base side ✓

Common Mistakes

Avoid these frequent errors

Assuming any line from vertex is height
Don't assume every line from a vertex to the opposite side is automatically a height = wrong triangle measurements! The line must be perpendicular to the base, not just touch it. Always check for the 90° angle or perpendicular symbol.

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 a right angle symbol (small square) where the line meets the base. In diagrams, this symbol indicates a 90° angle, confirming the line is the height.

What if the diagram doesn't show the right angle symbol clearly?

+

Sometimes diagrams assume you know geometric conventions. If the line appears to meet the base at a right angle and looks perpendicular, it's likely the height. Context clues help!

Can a triangle have more than one height?

+

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

Does the height always fall inside the triangle?

+

Not always! In obtuse triangles, some heights fall outside the triangle. The height line extends beyond the triangle to meet the extended base line perpendicularly.

Why is knowing the height important?

+

Triangle height is essential for calculating area using the formula: $Area = \frac{1}{2} \times base \times height$ . Without the correct height, your area calculation will be wrong!

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Geometric Analysis: Identifying the Correct Height of a Triangle

Triangle Height with Perpendicularity Verification

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