Triangle Altitude Verification: Is the Given Line a True Height?

Q: How can I tell if a line is perpendicular without measuring?

Look for the small square symbol at the intersection point! This symbol specifically indicates a 90° angle. In the figure, you can see this right angle marker where the line meets the base.

Q: Does the altitude always land inside the triangle?

No! In obtuse triangles, the altitude from the obtuse angle vertex will land outside the triangle on the extension of the opposite side. It's still a valid altitude.

Q: Can a triangle have more than one altitude?

Yes! Every triangle has exactly three altitudes - one from each vertex to the opposite side. All three altitudes intersect at a single point called the orthocenter.

Q: What if the triangle looks like it has a right angle already?

Even in right triangles, you still need to identify the altitude specifically. The legs of a right triangle are altitudes to each other, but there's also a third altitude from the right angle to the hypotenuse.

Q: Why is this line different from a median?

An altitude is perpendicular to the opposite side, while a median connects a vertex to the midpoint of the opposite side. They're usually different lines unless you have an isosceles triangle!

Triangle Altitudes with Perpendicular Line Verification

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

00:00 Determine whether the straight line in the drawing is 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 that is the solution to the question

Step-by-step written solution

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Understand the problem

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

Step-by-step solution

To determine if the straight line in the figure is the height of the triangle, we must verify the following:

The line segment must extend from a vertex of the triangle and be perpendicular to the opposite side (or its extension).

In examining the figure provided, we notice that the triangle is formed by vertices at points $A, B,$ and $C$ . Let's assume the base is the line segment $\overline{BC}$ .

The line in question extends from a vertex $A$ and appears to intersect the base $BC$ at a right angle.

Since it is extending from vertex to the opposite side and forming a right angle with it, this line meets the definition of an altitude.

Therefore, the line in the figure is indeed the height of the triangle. By confirming the perpendicular relationship, we determine that this geometric feature correctly describes an altitude.

Yes, the straight line in the figure is the height of the triangle.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Altitude extends from vertex perpendicular to opposite side
Technique: Check for right angle symbol at intersection point
Check: Verify line connects vertex to opposite side at 90° angle ✓

Common Mistakes

Avoid these frequent errors

Assuming any line from vertex is 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 for the perpendicular symbol or right angle marking.

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 perpendicular without measuring?

Look for the small square symbol at the intersection point! This symbol specifically indicates a 90° angle. In the figure, you can see this right angle marker where the line meets the base.

Does the altitude always land inside the triangle?

No! In obtuse triangles, the altitude from the obtuse angle vertex will land outside the triangle on the extension of the opposite side. It's still a valid altitude.

Can a triangle have more than one altitude?

Yes! Every triangle has exactly three altitudes - one from each vertex to the opposite side. All three altitudes intersect at a single point called the orthocenter.

What if the triangle looks like it has a right angle already?

Even in right triangles, you still need to identify the altitude specifically. The legs of a right triangle are altitudes to each other, but there's also a third altitude from the right angle to the hypotenuse.

Why is this line different from a median?

An altitude is perpendicular to the opposite side, while a median connects a vertex to the midpoint of the opposite side. They're usually different lines unless you have an isosceles triangle!

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Triangle Altitude Verification: Is the Given Line a True Height?

Triangle Altitudes with Perpendicular Line Verification

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How can I tell if a line is perpendicular without measuring?

Does the altitude always land inside the triangle?

Can a triangle have more than one altitude?

What if the triangle looks like it has a right angle already?

Why is this line different from a median?

🌟 Unlock Your Math Potential

More Questions

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Triangle Height Verification: Is the Given Line an Altitude?

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Triangle Height Verification: Analyzing the Altitude's Perpendicularity