Triangle Height Verification: Identifying the Perpendicular Line to Base

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

Look for right angle markers (small squares) where the line meets the base, or check if the line appears perfectly vertical when the base is horizontal. These visual clues indicate a 90° angle.

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: What if the height line extends outside the triangle?

That's normal for obtuse triangles! The height can extend beyond the triangle's boundary, as long as it's perpendicular to the extended base line.

Q: Does the height always go straight down?

Not always! Height appears vertical only when the base is horizontal. If you rotate the triangle, the height direction changes, but it's still the perpendicular line to the base.

Q: Why is this vertical line considered the triangle's height?

Because it starts at the top vertex, goes straight down to the base, and forms a 90° angle with the base (shown by the right angle marker). This meets the definition perfectly!

Triangle Heights 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

00:04 Let's find out if the straight line in the drawing is the height of the triangle.

00:08 Remember, a height starts at a vertex and goes straight down, making a right angle with the side.

00:15 So, this line is indeed the height! And that's how we solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

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 is the height of the triangle, we'll analyze its role within the triangle:

Step 1: Observe the triangle and the given line. The triangle seems to be made of three sides and a vertical line within it.
Step 2: Recall that the height of a triangle, in geometry, is defined as a perpendicular dropped from a vertex to the opposite side.
Step 3: Examine the positioning of the line: The vertical line starts at one vertex of the triangle and intersects the base, appearing to be perpendicular.
Step 4: Verify perpendicularity: Given that the line is shown as a clear vertical (and a small perpendicular indicator suggests perpendicularity), we accept this line as the height.
Step 5: Conclude with verification that the line is effectively meeting the definition of height for the triangle in the diagram.

Therefore, the vertical line in the figure is indeed the height of the triangle.

Yes

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Height is perpendicular line from vertex to opposite side
Visual Clues: Look for right angle markers and vertical positioning
Verification: Check that line connects vertex to base at 90° angle ✓

Common Mistakes

Avoid these frequent errors

Confusing any line inside triangle with height
Don't assume every line from vertex to opposite side is a height = wrong identification! The line must be perpendicular (90° angle) to the base. Always check for right angle markers or vertical positioning to confirm perpendicularity.

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 right angle markers (small squares) where the line meets the base, or check if the line appears perfectly vertical when the base is horizontal. These visual clues indicate a 90° angle.

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.

What if the height line extends outside the triangle?

That's normal for obtuse triangles! The height can extend beyond the triangle's boundary, as long as it's perpendicular to the extended base line.

Does the height always go straight down?

Not always! Height appears vertical only when the base is horizontal. If you rotate the triangle, the height direction changes, but it's still the perpendicular line to the base.

Why is this vertical line considered the triangle's height?

Because it starts at the top vertex, goes straight down to the base, and forms a 90° angle with the base (shown by the right angle marker). This meets the definition perfectly!

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Triangle Height Verification: Identifying the Perpendicular Line to Base

Triangle Heights 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 really perpendicular to the base?

Can a triangle have more than one height?

What if the height line extends outside the triangle?

Does the height always go straight down?

Why is this vertical line considered the triangle's height?

🌟 Unlock Your Math Potential

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