![]() It is used in various real-life scenarios such as architecture, engineering, and even in art. Understanding CPCTC can be a big step in your journey to mastering geometry. In simpler terms, if two triangles are congruent (exactly the same in size and shape), then their corresponding parts (sides and angles) are also congruent. If you’re wondering, ‘What does CPCTC stand for?’, it’s an abbreviation that stands for Corresponding Parts of Congruent Triangles are Congruent. One of the most interesting concepts in geometry is CPCTC. Geometry is a fascinating area of mathematics that involves shapes, sizes, and properties of space. ![]() That’s why it’s crucial for our students to grasp the essence of CPCTC, which establishes the congruence of corresponding parts in congruent triangles. Geometry, with its intricate shapes and spatial relationships, plays a vital role in numerous real-life applications, from designing buildings to creating stunning works of art. ![]() By understanding this fundamental principle, our young mathematicians at Brighterly will develop a solid foundation in geometry, logical reasoning, and problem-solving skills. In this article, we will embark on a journey through the definition, postulates, theorem, proof, and examples of CPCTC. At Brighterly, we believe in making math accessible, engaging, and tailored for young minds. Welcome to Brighterly, where learning mathematics is an exciting adventure! Today, we invite you to delve into the captivating world of geometry as we explore the concept of CPCTC – Corresponding Parts of Congruent Triangles are Congruent. Make line QR the subject of the formula by dividing both sides of the equation by the product of 10m and cos60° to get To find line QR when PR is given, we know that Ī r e a o f △ P Q R = P R ¯ × Q R ¯ × cos ( ∠ P R Q ) 60 m 2 = 10 m × Q R ¯ × cos 60 ° Ī r e a o f △ M O N = 60 m 2 A r e a o f △ P Q R = 60 m 2 Thus, with respect to the SAS theorem, we can say both triangles in III are congruent.ī) Based on the earlier solution from question a), we can say that only diagram II is SSS congruent.Ĭ) Based on the earlier solution from question a), we can say that both diagrams I and III are SAS congruent.ĭ) Since triangles MON and PQR are SAS congruent, i.e. In diagram III, both triangles have two of their sides and angle equal. In diagram II, all three sides of both angles are the same thus, in line with the SSS theorem, both triangles in diagram II are congruent. ![]() Thus, with respect to the SAS theorem, we can say both triangles in I are congruent. Determine the following:ĭ) If the area of the ΔMON is 60m 2, ∠PRQ is 60° and line PR is 10m find QR.Ī) From the figure above, diagram I have both triangles joined together have two of their sides and angle equal. The figure below consists of three diagrams labelled I, II and III. So let’s look at a case where it’s important to take into account the order in which we compare the sides of one triangle and the other in the next example.Īn image showing three diagrams of that portrays the SSS and SAS theorems - Vaia Original Why is this important? You can position the triangles in any way relative to each other and it will still be easy to tell that they are congruent, because all sides have the same length. The example above is a simple case because you don’t even need to look if the given sides are equal correspondingly, that is, whether the sides of one triangle are equal to the respective sides of the other triangle. We can say that the first triangle is congruent to the second triangle: You can look at the picture above to understand this better. So, Side-Side-Side – all three respective sides are equal between these triangles. This is a great case to apply the SSS theorem to prove congruence. So, by mere observation, it can be seen that both equilaterals are indeed the same (equal) in both length and angle. Two equilateral triangles - Vaia Original If you don’t know what is an equilateral triangle, this simply means a triangle with all equal sides. Two equilateral triangles are positioned next to each other.
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