Triangles are divided into two categories, namely triangles based on the side and triangles based on the corners.
Equilateral triangle
Equilaterally is formed by the combination of words, ie "Equi", which means identical and "lateral", which means facets.A equilateral triangle is also called a normal polygon or normal triangle when all sides and corners are identical.
- Triangle with all three comparable pages is known as oneequilateral triangle.
- Because all three sides are the same, the three respective corners are also the same.
- That is why every angle is 60 °.
Equilateral triangle
Read more:Corner formula
Like -legged Trheppant
A triangle with two sides of the same length, while the length of the third page is different as aLike -legged Trheppant.This measures the angle, which is located opposite the two straight sides, always the same.
- Set in a triangle ●ABC whose facets are AB and AC identical.
- Then ●ABC is a similar triangle where ∠ b = ∠ C.
- The expression that the similar triangle describes is "if the 2 facets of a triangle are congruent, then the angle that contradicts them is also congruent".
Read more:Congruence of triangles: rules and dissolved examples
Like -legged Trheppant
Read more:Angle between two lines
Uneven triangle
The Scalene Triangle is a triangle with all three different sides.When all three sides have different lengths, the corners are also different.
- However, the exclusive measurements have no influence on the sum of all inner cornersUnequal triangle.
- The sum of the 3 inner corners constantly adds up to 180 °, which meets the assets of posture in the triangle.
Uneven triangle
read more:Trigonometric identities
Right angular triangle
The right angular triangle is a triangle with one of the three corners exactly 90 °. The other two corners on a right -hand triangle are acute corners.Right angular triangleHas a hypotenuse that is the largest side and is always the opposite of the right angle.
Right angular triangle
Read more:Quadrangular corner feature
Acute corner triangle
An acute angular triangle is a triangle with all three corners less than 90 ° each.This of all corners on oneAcute corner triangleCalled acute corners.less than ninety ° °
Acute corner triangle
Read more:Area of a triangle
Stump/sloping corner triangle
The blunt angular triangle is Atrianus who has a corner that is always more than 90 °..
Stump/sloping corner triangle
Characteristics of a triangle
[Click here for examples of question]
The different characteristics of a triangle are as follows:
- The sum of all three corners on a triangle is 180 °.
- The sum of the lengths of two aspects of a triangle is usually more than the length of the third page.
- InOutdoor cornerFrom a triangle is the same as the sum of his interior opposite corners.
- The sum of all outside corners in each triangle is equal to 360 °.
- Two triangles are said to be the same as their corresponding sides and corners are the same.
- The circumference of a triangle is the same as the sum of all three sides of a triangle.
read more:Distance formula and disorder of coordinate geometry
Things to remember
- The properties of a triangle help us to study and identify a triangle in a closed figure.
- Similarly, the distinction between the lengths of each aspect of a triangle is usually less than the length of the third aspect.
- The aspect in contrast to the smallest interior corner is the shortest side and vice versa.
- Likewise, the site is opposite the largest inner corner is the longest facet and vice versa.
- In the case of a right -wing triangle, this aspect is known as hypotenuse.
- The top of a triangle is identical to the length of the perpendicular fall from a peak to the opposite aspect.
- This facet is taken into account by the base.
Examples of questions
Ques.What is the identifying characteristic of a rather corner triangle?(2 points)
Ans.One corner of a right angular triangle will always be measured as 90 °.
Ques.hill triangle all three sides have each other different from each other?(2 points)
Ans.Such a function is exhibited by a scaleen triangle.When all three sides have different lengths, the corners are also different.
Ques.What do you mean by a triangle?(3 points)
Ans.A triangle is actually a figure with three sides, three slabs and three corners.If you took the sum of all three corners in a triangle, it would be the same as 180 ° degrees.It is a three -sided polygon.
Ques.What is an equilateral triangle?(3 points)
Ans.Triangle with all three comparable sides is known as a equilateral triangle.When all three sides are the same, the three respective corners are also the same. "Equi", which means identical and "laterally", which means facets.A equilateral triangle is also called a normal polygon or normal triangle when all its aspects are identical.
Read more: Triangles important questions
Ques.What is the hypotenus at a right angle triangle?(3 points)
Ans.A hypotenuse in a right corner triangle is the largest side of the triangle and is always opposite the 90 ° corner.Even all corners are less than 90 °.
Also read:Corner between a line and a surface
Ques.What is an acute corner triangle?(3 points)
Ans.An acute angular triangle is a triangle with all three corners of less than 90 °. A lot less than a real perspective is an acute position.In the diagram we can see that each angle is less than 90 °. It can be slightly more than zero but less than 90 °.
Also read: Important comments from three -dimensional geometry
Ques.name The triangles based on their height on the sides?(3 points)
Ans.Triangles based on the length of their sides:
- Equal triangle: triangle, where all sides are straight, a like -sided triangle is called.
- Isosceles Triangle: Triangle, where two sides are straight, is called the triangle of Isoscel.
- Scalene Triangle: Triangle, where no sides are the same, are called the Scaleene Triangle.
Ques.name The triangles based on their inner corners?(3 points)
Ans.Triangles based on their inner corners:
- Right angle triangle: Triangle, where one of the corner is 90 degrees, is called the right angular triangle.
- Acute corner triangle: triangle, where all corners are less than 90 degrees, is called acute corner triangle.
- Stompe/sklik corner triangle: triangle, where all corners are larger than 90 degrees, is called bluntly angular triangle.
To ask.If ABC is a triangle where AB = 6 cm, BC = 7 cm and AC = 8 cm, find the circumference?(2 points)
Ans.Have, ABC is a triangle.
- AB = 6 cm
- BC = 7 cm
- AC = 8 cm
- As we know with the formula,
- Outline = sum of all three sides
- P = AB + BC + AC
- P = 6 + 7 + 8
- P = 21 cm
Ques.Find the area with a triangle with pages 5, 2 and 3 units length?(3 points)
Ans.Use the Herons formula to find the area with a triangle
- Semiperimeter (r) = (a + b + c)/2
- S = (5 + 2 +3)/2
- S = 5
- Surface of a triangle = √ [s (s-a) (s-b) (s-c)]
- √ [5 (5-5) (5-2) (5-3)]
- 0 square devices.
Questions. The purpose of two corners in a triangle is 60 degrees and 70 degrees.(3 points)
Ans.The dimensions of two corners on a triangle are calculated as follows:
- The sum of all three triangles after the corner sum = 180 degrees
- The sum of measuring two corners is indicated as 60 degrees and 70 degrees
- DUS that = 180 - 60-70
- Therefore the purpose of the third angle = 50 degrees
Ques.Find the lengths of the sides of a triangle if his corners are in the ratio of 2: 1: 3 and the circumference is 5 cm?(3 points)
Ans.According to the problem, the corners of the triangle are relatively 2: 1: 3 that the corners are 2k, K and 3K
Ie a = 2k, b = k at c = 3k.
- A + B + C = 180 °
- 2k + k + 3k = 180 °
- 6k = 180 °
- K = 30 °
- That is why the corners of the triangle are:
- A = 60 °, B = K = 30 ° en C = 3K = 90 °
- Round-ray = r = 5 cm.
Therefore, if the lengths of the sides of the triangle A, B, C are, then C is C
- A = 2 R sin a = 2 x 5x sin 60 ° = 5√3 cm.
- B = 2 r sin b = 2 x 5x sin 30 ° = 5 cm
- C = 2 R sin C = 2 x 5x sin 90 ° = 10 cm.
Questions. Of the corners of a triangle is 60 ° and the other two corners are comparable.(3 points)
Ans.The dimensions of two corners on a triangle are calculated as follows:
- The sum of all three triangle corners at the corner = 180 degrees.
- One of the corner is given as 60 degrees
- Let other two corners be equal to X, because both are the same
- Så 60 + x + x = 180
- X = 180-60
- X = 120
- x = 60 classes
- That is why the target of the two corners is 60 degrees
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