Introduction to Isosceles triangle definition
Going by geometry, the isosceles triangle definition states that any triangle with two sides and each of these sides are of equal length. In some cases, it is described as a triangle with two and just two sides of equal length
Isosceles triangle definition also identifies such as a triangle with at least two sides of equal length, this last definition as well as the equilateral triangle as a special case. By the isosceles triangle theorem, the two angles opposite the equal sides are as well equal, but if the third side is different then the third angle will as well not be the same
By the Steiner–Lehmus theorem, every triangle with two angle bisectors of equal length fall under the isosceles triangle definition
Depending on how you draw yours according to the isosceles triangle definition, it has two legs i.e. from the isosceles triangle definition we can see that the two long straight lines opposite each other and a base – the not too short but not long line which connects its legs together
An obtuse isosceles triangle definition with one angle that is obviously more than 90°
Solving an isosceles triangle definition with examples
Both the legs (the two opposite straight lines in the triangle) or the base of an isosceles triangle definition just like in any case where we are to find an unknown, can be determined if we know the other values. As we are already familiar with, the base of this isosceles triangle definition forms the height of the triangle with a perpendicular bisector right from the base
Now, this perpendicular line drawn from the base to reach its vertex in turn form another 2 similar right isosceles triangles definition. These two right angle triangles can be solved for using the Pythagoras’ theorem. It has been explained in details below:
- Finding the base of an isosceles triangle definition: in order to determine the base once we know its leg, height, we use the formula: Base = 2 √L2−A2, where: L = length of a leg of the isosceles triangle definition while A is the height or altitude
- Finding the leg isosceles triangle definition: to find the length of the length if we have its base and height, we use the formula: Leg = √A2 + (B2)2, where: letter B is the length of the triangle base and A is its altitude
- Altitude isosceles triangle definition: to find the height given the base and leg, use the formula: Altitude =√ L2−(B2)2, where: letter L is the length of a leg of the isosceles triangle definition while its base is letter B
Example 1: A right angled isosceles triangle definition with length 5 cm has a height of 13 cm. Find the area of this triangle:
- Let L be the length = 5 cm
- While H be its height = 13 cm
- The Formula to use is: Area A of the triangle = 12 (l × h) square unit i.e.
= 12 (5 x 13)
= 12 (65)
= 652
= 32.5. Therefore, the area of our triangle is: 32.5 cm2
Example 2: A right isosceles triangle definition has its length to be 7.5 m and height of 10 m. Find the area of that triangle:
- Let L be the length = 7.5 cm
- While H be its height = 10 cm
- The Formula to use is: Area A of the triangle = 12 (l × h) square unit i.e.
= 12 (7.5 x 10)
= 12 (75)
= 752
= 37.5. Therefore, the area of our triangle is: 37.5 cm2
Example 3: A right angled isosceles triangle definition has area 6.25 cm2 and length 2.5 cm. Find the height of the triangle:
- Let A be the area = 6.25 cm
- While L be its length = 2.5 cm
- The Formula to use is: Area A of the triangle = 12 (l × h) square unit i.e.
6.25 = 12 (2.5 x h)
6.25 = 1.25h
h= 6.251.25
= 5cm. Therefore, Height of our triangle is: 5 cm
Example 4: Solve the area of the obtuse isosceles triangle definition for the given base is 8 inches and height is 10 inches:
- Base = 8 inches
- Height = 10 inches
- Area A of obtuse isosceles triangle definition = 12 (Base × Height)
- Area = 12 x 8 x 10 = 40. Therefore, the area of an obtuse isosceles triangle definition is 40 square inches
Example 5: find the area of obtuse isosceles triangle definition for the given base is 10 meters and height is 6 meters?:
- Base = 10 meters
- Height = 6 meters
- Area A of obtuse triangle = 12 (Base × Height)
- Area = 12 × 10 × 6 = 30. Therefore, the area of an obtuse triangle is 30m2
Example 6: Solve the area of an obtuse triangle if the given base is 15 centimeters and height is 7.5 centimeters?:
- Base = 15 centimeter
- Height = 7.5 centimeter
- Area A of obtuse triangle = 12 (Base × Height)
- Area = 12 × 15 × 7.5 = 56.25 Therefore, the area of an obtuse triangle is 56.25 cm2
Example 7: If the two interior angles of the acute triangle are 750 and 500 respectively, solve for the third interior angle of the triangle:
- Both internal angles are 750 and 500
- Sum of the internal angles in acute triangle is 1800
- Imagine the third angle p0 since all triangles regardless of their type must have three sides or three angles
- Therefore, we have: 750 + 500 + our 3rd angle p0 = 1800
- 1250 + p0 = 1800
- p0 = 1800 – 1250
- p0 = 550. Our 3rd inner angle of the acute triangle is: 550
Example 8: Solve for the outer angle of the acute angled triangle when the two inner opposite angles are 500 and 800 respectively:
- Since both the outer and inner angles are added up to form the angles within a triangle, therefore, we have: 500 + 800 = 1300. Finally, the external angle of this acute triangle will be 1300
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