When two lines are perpendicular, it means they intersect or meet each other at a perfect right angle, which is 90 degrees. Imagine the corner of a square or the intersection of a wall and the floor; those are examples of perpendicular lines. This term is often used in subjects like geometry and science to describe objects or lines that are perfectly straight up and down or side to side in relation to each other. So, if you hear that two things are perpendicular, you know they form a precise, square corner.
In geometric contexts, perpendicular lines or planes intersect to form right angles, signifying a precise 90-degree relationship. This fundamental concept is crucial across various scientific and mathematical disciplines, serving as a bedrock for understanding spatial arrangements and structural integrity. For instance, in architecture and engineering, perpendicularity ensures stability and alignment in constructions. Moreover, in advanced mathematics, the notion extends to orthogonal vectors and subspaces, underpinning principles in linear algebra and calculus. Thus, a firm grasp of perpendicularity is indispensable for rigorous analysis and problem-solving in complex systems.
§ Understanding 'Perpendicular'
The word perpendicular is quite specific in its meaning, especially in geometry and technical contexts. It describes a very precise relationship between two lines, surfaces, or objects: they meet or cross at a perfect 90-degree angle. This means they are 'square' to each other, forming a right angle. Because of this exactness, there aren't many direct synonyms that can be used interchangeably in all situations without losing some of that precision. However, depending on the context, there are words that can convey a similar idea of alignment or orientation.
The engineer checked to make sure the two beams were perpendicular before welding them together.
§ Similar Concepts and When to Use Them
- Right Angle
- This is perhaps the closest concept to perpendicular. A right angle is the 90-degree angle itself. When two lines are perpendicular, they form a right angle. You might use 'right angle' when describing the angle itself, rather than the relationship between the lines.
The corner of the room formed a perfect right angle.
- Orthogonal
- This is a more technical and mathematical term that is often used as a synonym for perpendicular, especially in higher-level geometry, linear algebra, and signal processing. While perpendicular typically refers to lines or planes in Euclidean space, orthogonal can have broader applications, including vectors and functions. For everyday language, perpendicular is usually preferred.
In this coordinate system, the x, y, and z axes are orthogonal to each other.
- At 90 Degrees / At a Right Angle
- These are descriptive phrases that convey the same meaning as perpendicular without using the specific word. They are useful when you want to explain the concept in simpler terms or avoid technical jargon. For instance, you might say "The shelves are mounted at 90 degrees to the wall."
The two roads intersect at a right angle.
- Vertical / Horizontal
- While not direct synonyms, 'vertical' and 'horizontal' often describe lines that are perpendicular to each other in a standard coordinate system or in relation to the ground. A vertical line goes straight up and down, and a horizontal line goes straight across. They are perpendicular if one is truly upright and the other is truly level.
The wall is vertical, and the floor is horizontal, making them perpendicular.
§ When to Use 'Perpendicular'
You should use the word perpendicular when precision is important and you want to specifically communicate that two lines, planes, or surfaces intersect at exactly a 90-degree angle. This is especially true in:
- Mathematics and Geometry: This is where the term is most frequently and precisely used.
- Science and Engineering: When describing structures, forces, or experimental setups where exact angles are crucial.
- Architecture and Construction: To ensure that corners are square, walls are straight, and foundations are level.
- Technical Instructions: When giving directions for assembly or alignment where accuracy is key.
While alternatives like 'at a right angle' or 'square' can sometimes be used in less formal contexts, perpendicular remains the most accurate and universally understood term for this specific geometric relationship.
按水平分级的例句
The two roads are perpendicular.
Las dos carreteras son perpendiculares.
Draw a perpendicular line.
Dibuja una línea perpendicular.
The wall is perpendicular to the floor.
La pared es perpendicular al suelo.
The cross makes a perpendicular shape.
La cruz forma una figura perpendicular.
Are these lines perpendicular?
¿Son perpendiculares estas líneas?
The flag pole is perpendicular to the ground.
El mástil es perpendicular al suelo.
The table legs are perpendicular to the top.
Las patas de la mesa son perpendiculares a la parte superior.
We need to make it perpendicular.
Necesitamos hacerlo perpendicular.
In Euclidean geometry, perpendicular lines are fundamental for constructing right angles and defining orthogonal relationships between objects.
In Euclidean geometry, lines that meet at a 90-degree angle are essential for building right angles and showing how objects relate orthogonally.
This sentence uses a formal and academic tone, typical of C1 level English, with complex grammatical structures such as 'for constructing... and defining...'.
The architect ensured that all vertical supports were perfectly perpendicular to the horizontal beams, guaranteeing structural integrity.
The architect made sure all up-and-down supports were exactly at right angles to the side beams, so the building would be strong.
The use of 'ensured that' and 'guaranteeing structural integrity' demonstrates a higher level of vocabulary and complex sentence structure.
Students learned to calculate the slope of a line perpendicular to a given equation, a crucial concept in analytical geometry.
Students learned how to find the steepness of a line that is at a right angle to a certain equation, which is a very important idea in geometry that uses coordinates.
This sentence incorporates specialized vocabulary ('analytical geometry') and a more abstract concept, characteristic of C1.
For precise measurements, it's imperative that the measuring tape is held perpendicular to the surface being measured, avoiding parallax errors.
To measure accurately, it's very important to hold the measuring tape at a right angle to the surface you're measuring, so you don't make mistakes from looking at it wrong.
The phrase 'it's imperative that' and the inclusion of a technical term like 'parallax errors' elevates the linguistic complexity to C1.
The artist positioned the frame such that its edges were perfectly perpendicular to the gallery wall, creating a sense of visual harmony.
The artist placed the frame so its sides were exactly at right angles to the gallery wall, making it look balanced.
This sentence employs descriptive language and a causal relationship ('such that... creating a sense of...'), indicating C1 proficiency.
When setting up the experiment, ensure the sensor is mounted perpendicular to the direction of the fluid flow for optimal data collection.
When preparing the experiment, make sure the sensor is put in place at a right angle to how the liquid is moving, to get the best information.
The use of 'optimal data collection' and the imperative 'ensure' within a scientific context are indicators of C1 level.
The surveyor used advanced laser technology to confirm that the boundaries of the property were truly perpendicular, preventing future disputes.
The surveyor used new laser tools to check that the property lines were truly at right angles, which stopped arguments later.
This sentence integrates specific professional terminology ('surveyor,' 'laser technology') and describes a preventative action ('preventing future disputes'), suitable for C1.
Despite the uneven terrain, the skilled construction crew managed to erect the temporary structure with its main support beams perpendicular to the ground.
Even though the land was bumpy, the good construction workers were able to build the temporary structure with its main support beams at right angles to the ground.
The use of a concessive clause ('Despite the uneven terrain') and a more sophisticated verb like 'erect' are characteristic of C1 English.
近义词
反义词
自我测试 18 个问题
Draw two lines that are perpendicular. Write one sentence to describe your drawing.
Well written! Good try! Check the sample answer below.
Sample answer
My drawing shows two lines. The lines are perpendicular because they meet at a 90-degree angle.
Imagine you are building a small house with toy blocks. How would you use perpendicular lines to make the walls strong? Write a short sentence.
Well written! Good try! Check the sample answer below.
Sample answer
I would make the walls perpendicular to the floor to make them straight.
Look around your room. Can you find two things that are perpendicular to each other? Write one sentence about what you see.
Well written! Good try! Check the sample answer below.
Sample answer
The wall and the floor are perpendicular in my room.
What kind of angle do perpendicular lines make?
Read this passage:
A perpendicular line is like a corner of a square. When two lines meet at a perfect corner, they are perpendicular. This means they make a 90-degree angle. This word is often used in math and when talking about building things.
What kind of angle do perpendicular lines make?
The passage states that perpendicular lines make a 90-degree angle.
The passage states that perpendicular lines make a 90-degree angle.
What can be perpendicular when you fold a piece of paper?
Read this passage:
Imagine you have a big piece of paper. If you fold the paper exactly in half, the fold line and the edge of the paper can be perpendicular. This is because they meet at a perfect right angle.
What can be perpendicular when you fold a piece of paper?
The passage says 'the fold line and the edge of the paper can be perpendicular'.
The passage says 'the fold line and the edge of the paper can be perpendicular'.
What is a good example of perpendicular lines?
Read this passage:
When you draw a cross '+' on a paper, the lines are perpendicular. This is a good example of how they look. They cross each other to make perfect square corners.
What is a good example of perpendicular lines?
The passage directly states that 'when you draw a cross '+' on a paper, the lines are perpendicular'.
The passage directly states that 'when you draw a cross '+' on a paper, the lines are perpendicular'.
Which of these is an example of a perpendicular line?
Perpendicular lines meet at a perfect 90-degree angle, like the shape of a 'T'.
If two lines are perpendicular, what kind of angle do they make when they meet?
The definition of perpendicular lines is that they meet at a 90-degree angle.
In which subject do you most often hear the word 'perpendicular'?
The word 'perpendicular' is commonly used in math and science to describe geometric relationships between lines.
Perpendicular lines always cross each other.
For lines to be perpendicular, they must meet or cross at a 90-degree angle.
If two lines are parallel, they are also perpendicular.
Parallel lines never meet, while perpendicular lines meet at a 90-degree angle. They are opposite concepts.
The corner of a square room is an example of perpendicular lines.
The walls of a square room meet at a 90-degree angle, making them perpendicular.
Which of the following describes two lines that are perpendicular?
Perpendicular lines are defined as lines that meet or cross at a 90-degree angle, creating a 'perfectly square' intersection.
In a geometry problem, if line A is perpendicular to line B, what can we conclude about their intersection?
A right angle is exactly 90 degrees, which is the defining characteristic of perpendicular lines.
Imagine a wall and the floor of a room. How do they typically relate to each other in terms of being perpendicular?
In most standard building constructions, walls meet floors at a 90-degree angle, making them perpendicular.
If two lines are perpendicular, they must be straight lines.
The concept of perpendicularity applies specifically to straight lines or planes. Curved lines cannot be perpendicular in the same way.
Two lines that cross at an acute angle are perpendicular.
Perpendicular lines cross at a 90-degree (right) angle, not an acute angle (which is less than 90 degrees).
The word 'perpendicular' is primarily used in the context of advanced literature.
The definition states that 'perpendicular' is used in science and math, not primarily in literature.
/ 18 correct
Perfect score!
例句
The carpenter used a tool to make sure the wall was a perfect perpendicular to the floor.
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