Scalene triangle

Scalene triangles Here you will learn about scalene triangles, including what a scalene triangle is and the properties of scalene triangles. Students first learn about triangles in kindergarten and 1st grade in geometry with their work in reason with shapes and their attributes. They expand their knowledge of triangles as they progress through elementary school and into secondary school. What is a scalene triangle? A scalene triangle is a type of triangle that has no equal side lengths and no equal angle measurements, which means the sides and angles are not congruent. Properties of a scalene triangle: • No equal sides. • No equal angles. The dash marks on the sides and the angles do not match up. This shows that the triangle does not have congruent sides and does not have congruent angles. There are three types of scalene triangles: Common Core State Standards How does this apply to 4th grade and 5th grade math? • Grade 4 – Geometry (4.G.A.3) Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. • Grade 5 – Geometry (5.G.B.3) Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Example 1: classify scalene triangle Select the triangle that is scalene. • Recall the definition. A scalene triangle is a triangle that has no equal sides and no...

Contents • 1 Area • 2 Perimeter • 3 Trigonometric functions of half angles in a triangle • 4 Trigonometric functions of whole angles in a triangle • 5 CircumCircle • 6 InCircle Area [ ] The area of a scalene triangle is: A = ( a 2 + b 2 + c 2 ) 2 − 2 ( a 4 + b 4 + c 4 ) 4

Two principal areas of nerve compression in neurogenic TOS are the scalene triangle and the subpectoralis space. The scalene triangle is bound by the anterior and middle scalene muscles, with the first rib at the base. The brachial plexus nerves (yellow) and the subclavian artery (red) pass through the scalene triangle, while the subclavian vein (blue) passes in front. Beyond the first rib and clavicle, the brachial plexus nerves, subclavian artery and subclavian vein all pass underneath the pectoralis minor muscle, in front of the shoulder. Below the skin in the lower neck is a thick layer of fatty tissue called the scalene fat pad, which helps to protect the deeper muscular and neurovascular structures of the thoracic outlet. The presence of the scalene fat pad also makes it difficult to feel the structures of the thoracic outlet when pressing with the fingers on the lower neck. Part of the omohyoid muscle, a small muscle that runs across the lower part of the neck, passes through the scalene fat pad. Directly behind the scalene fat pad lies the anterior scalene muscle. This muscle arises from the cervical spine vertebrae and runs vertically to attach to the top of the anterior first rib. Another muscle in this area is the middle scalene muscle. This muscle also arises from the cervical spine vertebrae and runs vertically, attaching to the top of the mid-portion of the first rib. The narrow vertical space formed between the two scalene muscles, with the first rib at the ...

A triangle in which all three sides are of different lengths and all the three angles of the triangle are also of different measures, is called a scalene triangle . In comparison an isosceles triangle has two equal sides and an equilateral triangle has three equal sides. A scalene triangle with three vertices, A, B , and C , is represented as \(\triangle ABC\) Therefore, it is clear from this image of a scalene triangle that, AB ≠ BC ≠ CA . • All the sides of the scalene triangle are unequal. • All the angles of the scalene triangle are unequal. • As it has no equal sides, hence there is no line of symmetry. • It has no point of symmetry. • A scalene triangle can be an acute angle, an obtuse angle or a right angle triangle. • The formula for the area of a scalene triangle is: A = \(\sqrt\) Example 1: Classify the triangle based on its sides. Solution: From the figure, sides of the triangle are 7 cm, 15 cm and 12 cm. All the sides of the triangle are unequal in length that is 7 ≠ 12 ≠ 15 Hence, it is a scalene triangle. Example 2: Classify the triangular park according to its sides and then determine the park’s perimeter. Solution: From the figure- Sides of the triangular park are 40 m, 60 m and 90 m So, all sides of the triangular park are not in the same length. As a result, it’s a scalene triangle. To determine its perimeter, find the sum of all the side lengths of the park. 90 + 60 + 40 = 190 Hence, the perimeter of the triangular park is 190 meters. Example 3: Classify...

Synonyms: Anterior scalene muscle, Musculi scaleni anteriores The scalene muscles are the three muscles found on each side of the lateral vertebral muscle group. The main functions of these muscles are Key facts about scalene muscles Anterior scalene muscle Origin: anterior tubercle of transverse processes of vertebrae C3-C6 Insertion: anterior scalene tubercle of rib 1, superior border of rib 1 (anterior to subclavian groove) Innervation: anterior rami of spinal nerves C4-C6 Blood supply: ascending cervical branch of the inferior thyroid artery. Function: - bilateral contraction - neck flexion - unilateral contraction - neck lateral flexion (ipsilateral), neck rotation (contralateral), elevates rib 1 Middle scalene muscle Origin: transverse processes of C1/C2 -> C7 (specifically posterior tubercles of transverse processes of vertebrae in C3-C7) Insertion: superior border of rib 1 (posterior to subclavian groove) Innervation: anterior rami of spinal nerves C3-C8 Blood supply: ascending cervical branch of the inferior thyroid artery Function: neck lateral flexion, elevates rib 1 Posterior scalene muscle Origin: posterior tubercles of transverse processes of vertebrae C4-C6/C5-C7 Insertion: external surface of rib 2 Innervation: anterior rami of spinal nerves C6-C8 Blood supply: ascending cervical branch of the inferior thyroid artery; superficial cervical artery Function: neck lateral flexion, Elevates rib 2 This article will discuss the Synonyms: Anterior scalene muscle, M...

More • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Types Of Triangles There are basically six different types of triangles with respect to the length and measure of the lines and angles of a triangle, respectively. To recall, a triangle is a specific type of polygon having only three sides and three angles. Based on these specifications and design, the As the name suggests, a “triangle” is a three-sided polygon having three angles. The sum of all interior angles of a triangle will always add up to 180 degrees. This is called the Also check: Table of contents: • • • • • • • • • Six Types of Triangles Triangles can be broadly classified into two types, which are: • Triangles based on the lengths of their sides • Triangles based on their interior angles These two triangle types are explained here along with their furth...

Synonyms: Trigonum cervicale anterius The  triangles of the neck are the topographic areas of the The triangles of the neck are important because of their contents, as they house all the neck structures, including glands, nerves, vessels and lymph nodes. For that reason, this article will discuss the anatomy, borders and contents of the triangles of the neck. Key facts about the triangles of the neck Definition Two triangular areas found anterior and posterior to the sternocleidomastoid muscles which contain the visceral structures of the neck. Anterior triangle Borders: - Superior - inferior border of mandible - Medial - midline of neck - Lateral - anterior border of sternocleidomastoid muscle Subdivisions: - Muscular (omotracheal) triangle - Carotid triangle - Submandibular triangle - Submental triangle Posterior triangle Borders: - Anterior - posterior margin of sternocleidomastoid muscle - Posterior - anterior margin of trapezius muscle - Inferior - middle one-third of clavicle Subdivisions: - Occipital triangle - Supraclavicular (omoclavicular) triangle Anatomical triangles The median line of the neck divides the neck into symmetrical halves. The sternocleidomastoid muscle, in its oblique (posterosuperior) course, further divides the neck into anterior and posterior triangles. The anterior triangle of the neck is further subdivided into four smaller triangles, while the posterior triangle is broken up into two smaller triangles. Master the triangles of the nec...

An acute \blueD acute triangles start color #11accd, start text, a, c, u, t, e, space, t, r, i, a, n, g, l, e, s, end text, end color #11accd . A right \purpleD right triangles start color #7854ab, start text, r, i, g, h, t, space, t, r, i, a, n, g, l, e, s, end text, end color #7854ab . An obtuse \greenD obtuse triangles start color #1fab54, start text, o, b, t, u, s, e, space, t, r, i, a, n, g, l, e, s, end text, end color #1fab54 . An equilateral \blueD equilateral start color #11accd, start text, e, q, u, i, l, a, t, e, r, a, l, end text, end color #11accd triangles. An isosceles \purpleD isosceles start color #7854ab, start text, i, s, o, s, c, e, l, e, s, end text, end color #7854ab triangles. A scalene \greenD scalene start color #1fab54, start text, s, c, a, l, e, n, e, end text, end color #1fab54 triangles.