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What is the Pythagorean theorem and the altitude theorem?
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a^2 + b^2 = c^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. The altitude theorem, also known as the geometric mean theorem, states that in a right-angled triangle, the altitude (the perpendicular line from the right angle to the hypotenuse) is the geometric mean between the two segments of the hypotenuse. This can be expressed as h^2 = p * q, where h is the length of the altitude, and p and q are the lengths of the two segments of the hypotenuse. **
What is the Pythagorean theorem and the cathetus theorem?
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be written as a^2 + b^2 = c^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides, called catheti. The cathetus theorem, also known as the converse of the Pythagorean theorem, states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right-angled triangle. In other words, if a^2 + b^2 = c^2, then the triangle is a right-angled triangle, where c is the longest side (hypotenuse) and a and b are **
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Adobe Acrobat Standard DC (Subscription) - 1 MonthAcrobat Standard DC is the subscription version of the Adobe programme, used to convert, crop, edit, sign and manage PDF documents. Acrobat Standard DC includes 100 GB of space on Adobe cloud for your external storage. This version is on subscription (monthly, quarterly or annual) if you are looking for a version without any expiry date, you can find it by purchasing products with a perpetual licence such as Adobe Acrobat Pro 2020 or Adobe Acrobat 2019. What is included in Adobe Acrobat Standard DC? By purchasing a subscription licence for Adobe Acrobat Standard DC you have access to the following features: PDF creation and conversion - allows you to convert Word, Excel, Powerpoint and image files into PDF files Export to other formats - to convert your PDFs into any format Direct editing - to intervene directly on files and modify them Electronic signature - to apply your digital signature and guarantee the authenticity of documents Cloud storage space - 100 GB of storage on Adobe cloud Additionally, you also have access to the installation guide provided with the Adobe Acrobat Standard DC subscription, sent via e-mail immediately after your purchase. Adobe Acrobat Standard DC: differences with other versions Adobe Standard DC includes all basic PDF functionality, these include: editing and organising PDF files; converting documents to and from PDF; form completion, document signing and requesting electronic signatures; protecting files via password. Compared to the Pro DC version of Adobe software, it lacks the OCR tool, redaction, generative AI implementation and advanced features that you can instead find in the more expensive subscription. Compared instead to the perpetual licence edition, namely Acrobat Pro 2020 and earlier versions, it boasts continuous updates to keep the software always at the latest version, as well as compatibility with macOS. Adobe Acrobat: which one to choose in brief? The Acrobat software is available in three different formats: two of these are on subscription, such as Acrobat Standard DC, whilst one has a perpetual licence. Below are the characteristics of each of them. Feature Acrobat Standard DC Acrobat Pro DC Acrobat Pro 2020 Licence type Subscription (monthly, quarterly, annual) Subscription (monthly, quarterly, annual) Perpetual (one-time) Operating systems Windows, macOS Windows, macOS Windows Devices 1 2 (not for concurrent use) 1 Cloud Storage 100 GB 100 GB — Advanced features — (editing, conversion, digital signature) ✓ (OCR, redaction, preflight, batch + generative AI) ✓ (OCR, redaction, preflight, batch) Updates ✓ Continuous ✓ Continuous — The choice depends on your usage needs. If you need to use Acrobat for collaborative and work purposes, then you can consider purchasing Acrobat Standard DC or Acrobat Pro DC, both versions guarantee 100 GB of cloud storage and all the most useful features for managing and editing PDFs. In the event that you need desktop software, with no expiry date and without the...10,90 £*Shipping: 0,00 £Secure redirect to the provider
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How can the altitude theorem and the cathetus theorem be transformed?
The altitude theorem and the cathetus theorem can be transformed by applying them in different geometric shapes and contexts. For example, the altitude theorem, which states that the length of the altitude of a triangle is inversely proportional to the length of the corresponding base, can be applied to various types of triangles and even extended to other polygons. Similarly, the cathetus theorem, which relates the lengths of the two perpendicular sides of a right triangle to the length of the hypotenuse, can be generalized to other right-angled shapes or even applied in three-dimensional geometry. By exploring different scenarios and shapes, these theorems can be adapted and transformed to solve a wide range of geometric problems. **
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What are the altitude theorem and the cathetus theorem of Euclid?
The altitude theorem of Euclid states that in a right-angled triangle, the square of the length of the altitude drawn to the hypotenuse is equal to the product of the lengths of the two segments of the hypotenuse. This theorem is also known as the geometric mean theorem. The cathetus theorem of Euclid states that in a right-angled triangle, the square of the length of one of the catheti (the sides that form the right angle) is equal to the product of the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that cathetus. This theorem is also known as the Pythagorean theorem. Both the altitude theorem and the cathetus theorem are fundamental principles in the study of geometry and are essential for understanding the properties of right-angled triangles. **
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What is Thales' theorem?
Thales' theorem states that if A, B, and C are points on a circle where the line AC is a diameter, then the angle at B is a right angle. In other words, if a triangle is inscribed in a circle with one of its sides being the diameter of the circle, then that triangle is a right triangle. Thales' theorem is a fundamental result in geometry and is named after the ancient Greek mathematician Thales of Miletus. **
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What is the difference between proportionality theorem 1 and proportionality theorem 2?
Proportionality theorem 1 states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. Proportionality theorem 2, on the other hand, states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side of the triangle. In essence, theorem 1 deals with parallel lines and their proportional divisions within a triangle, while theorem 2 deals with proportional divisions and the parallelism of lines within a triangle. **
What is the formula for the altitude theorem and the cathetus theorem?
The formula for the altitude theorem is: \( a^2 = x \cdot (x + h) \), where \( a \) is the length of the hypotenuse, \( x \) is the length of one of the legs, and \( h \) is the length of the altitude drawn to the hypotenuse from the right angle. The formula for the cathetus theorem is: \( x \cdot y = h^2 \), where \( x \) and \( y \) are the lengths of the two legs of the right triangle, and \( h \) is the length of the altitude drawn to the hypotenuse from the right angle. **
What is the proof for the altitude theorem and the cathetus theorem?
The altitude theorem states that in a right triangle, the altitude drawn from the right angle to the hypotenuse creates two similar triangles with the original triangle. This can be proven using the properties of similar triangles and the Pythagorean theorem. The cathetus theorem states that the two legs of a right triangle are proportional to the segments of the hypotenuse that they create when an altitude is drawn from the right angle. This can also be proven using the properties of similar triangles and the Pythagorean theorem. **
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What is the Pythagorean theorem and the altitude theorem?
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a^2 + b^2 = c^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. The altitude theorem, also known as the geometric mean theorem, states that in a right-angled triangle, the altitude (the perpendicular line from the right angle to the hypotenuse) is the geometric mean between the two segments of the hypotenuse. This can be expressed as h^2 = p * q, where h is the length of the altitude, and p and q are the lengths of the two segments of the hypotenuse. **
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What is the Pythagorean theorem and the cathetus theorem?
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be written as a^2 + b^2 = c^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides, called catheti. The cathetus theorem, also known as the converse of the Pythagorean theorem, states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right-angled triangle. In other words, if a^2 + b^2 = c^2, then the triangle is a right-angled triangle, where c is the longest side (hypotenuse) and a and b are **
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How can the altitude theorem and the cathetus theorem be transformed?
The altitude theorem and the cathetus theorem can be transformed by applying them in different geometric shapes and contexts. For example, the altitude theorem, which states that the length of the altitude of a triangle is inversely proportional to the length of the corresponding base, can be applied to various types of triangles and even extended to other polygons. Similarly, the cathetus theorem, which relates the lengths of the two perpendicular sides of a right triangle to the length of the hypotenuse, can be generalized to other right-angled shapes or even applied in three-dimensional geometry. By exploring different scenarios and shapes, these theorems can be adapted and transformed to solve a wide range of geometric problems. **
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What are the altitude theorem and the cathetus theorem of Euclid?
The altitude theorem of Euclid states that in a right-angled triangle, the square of the length of the altitude drawn to the hypotenuse is equal to the product of the lengths of the two segments of the hypotenuse. This theorem is also known as the geometric mean theorem. The cathetus theorem of Euclid states that in a right-angled triangle, the square of the length of one of the catheti (the sides that form the right angle) is equal to the product of the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that cathetus. This theorem is also known as the Pythagorean theorem. Both the altitude theorem and the cathetus theorem are fundamental principles in the study of geometry and are essential for understanding the properties of right-angled triangles. **
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Canva Pro Education - 1 year SubscriptionWhen you make a purchase, you will receive an e-mail to subscribe to Canva Education , which will give you access to all the professional features of Canva Pro + 1800 free neutral Instagram post templates Please note: Brand Kite and Canva AI are not included How to Copy a Project from Your Personal Canva Account to a Canva Pro Class Account Discover the power of professional design with our annual subscription to Canva Pro. With Canva Pro, you'll have access to a wide range of premium tools and resources that will allow you to create stunning visual content for your business, personal projects, and more. Here's what you can expect with a year of Canva Pro: Unlimited access to over 100 million premium resources: Images, video, audio, graphics, and more, all ready to be used in your projects. Customisable templates: Thousands of high-quality templates for every need, from presentations to social media posts, from flyers to business cards. Advanced design tools: Features such as one-click background removal, the creation of customised brand kits, and the ability to resize your designs with a single click. Real-time collaboration: Work together with your team, leaving comments and suggestions directly in the projects, for seamless collaboration. Direct publication on social media: Schedule and publish your content directly from Canva on all major social platforms. Unlimited cloud storage: Save and organise all your projects in one place, with unlimited space. Don't miss the opportunity to take your design to the next level. With Canva Pro, the possibilities are endless. Subscribe now and start creating like a pro! How come the licence is priced so low? We offer retail licences that are used and discontinued by the previous owner since the EC ruling C-128/2011. That is why you can purchase the official licence on our site at a cheaper price. This is a product in STUDENT Version.6,87 £*Shipping: 0,00 £Secure redirect to the provider
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Adobe Acrobat Standard DC (Subscription) - 1 MonthAcrobat Standard DC is the subscription version of the Adobe programme, used to convert, crop, edit, sign and manage PDF documents. Acrobat Standard DC includes 100 GB of space on Adobe cloud for your external storage. This version is on subscription (monthly, quarterly or annual) if you are looking for a version without any expiry date, you can find it by purchasing products with a perpetual licence such as Adobe Acrobat Pro 2020 or Adobe Acrobat 2019. What is included in Adobe Acrobat Standard DC? By purchasing a subscription licence for Adobe Acrobat Standard DC you have access to the following features: PDF creation and conversion - allows you to convert Word, Excel, Powerpoint and image files into PDF files Export to other formats - to convert your PDFs into any format Direct editing - to intervene directly on files and modify them Electronic signature - to apply your digital signature and guarantee the authenticity of documents Cloud storage space - 100 GB of storage on Adobe cloud Additionally, you also have access to the installation guide provided with the Adobe Acrobat Standard DC subscription, sent via e-mail immediately after your purchase. Adobe Acrobat Standard DC: differences with other versions Adobe Standard DC includes all basic PDF functionality, these include: editing and organising PDF files; converting documents to and from PDF; form completion, document signing and requesting electronic signatures; protecting files via password. Compared to the Pro DC version of Adobe software, it lacks the OCR tool, redaction, generative AI implementation and advanced features that you can instead find in the more expensive subscription. Compared instead to the perpetual licence edition, namely Acrobat Pro 2020 and earlier versions, it boasts continuous updates to keep the software always at the latest version, as well as compatibility with macOS. Adobe Acrobat: which one to choose in brief? The Acrobat software is available in three different formats: two of these are on subscription, such as Acrobat Standard DC, whilst one has a perpetual licence. Below are the characteristics of each of them. Feature Acrobat Standard DC Acrobat Pro DC Acrobat Pro 2020 Licence type Subscription (monthly, quarterly, annual) Subscription (monthly, quarterly, annual) Perpetual (one-time) Operating systems Windows, macOS Windows, macOS Windows Devices 1 2 (not for concurrent use) 1 Cloud Storage 100 GB 100 GB — Advanced features — (editing, conversion, digital signature) ✓ (OCR, redaction, preflight, batch + generative AI) ✓ (OCR, redaction, preflight, batch) Updates ✓ Continuous ✓ Continuous — The choice depends on your usage needs. If you need to use Acrobat for collaborative and work purposes, then you can consider purchasing Acrobat Standard DC or Acrobat Pro DC, both versions guarantee 100 GB of cloud storage and all the most useful features for managing and editing PDFs. In the event that you need desktop software, with no expiry date and without the...10,90 £*Shipping: 0,00 £Secure redirect to the provider
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What is Thales' theorem?
Thales' theorem states that if A, B, and C are points on a circle where the line AC is a diameter, then the angle at B is a right angle. In other words, if a triangle is inscribed in a circle with one of its sides being the diameter of the circle, then that triangle is a right triangle. Thales' theorem is a fundamental result in geometry and is named after the ancient Greek mathematician Thales of Miletus. **
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What is the difference between proportionality theorem 1 and proportionality theorem 2?
Proportionality theorem 1 states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. Proportionality theorem 2, on the other hand, states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side of the triangle. In essence, theorem 1 deals with parallel lines and their proportional divisions within a triangle, while theorem 2 deals with proportional divisions and the parallelism of lines within a triangle. **
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What is the formula for the altitude theorem and the cathetus theorem?
The formula for the altitude theorem is: \( a^2 = x \cdot (x + h) \), where \( a \) is the length of the hypotenuse, \( x \) is the length of one of the legs, and \( h \) is the length of the altitude drawn to the hypotenuse from the right angle. The formula for the cathetus theorem is: \( x \cdot y = h^2 \), where \( x \) and \( y \) are the lengths of the two legs of the right triangle, and \( h \) is the length of the altitude drawn to the hypotenuse from the right angle. **
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What is the proof for the altitude theorem and the cathetus theorem?
The altitude theorem states that in a right triangle, the altitude drawn from the right angle to the hypotenuse creates two similar triangles with the original triangle. This can be proven using the properties of similar triangles and the Pythagorean theorem. The cathetus theorem states that the two legs of a right triangle are proportional to the segments of the hypotenuse that they create when an altitude is drawn from the right angle. This can also be proven using the properties of similar triangles and the Pythagorean theorem. **
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