Properties of Equilateral Triangle
- All three sides are equal.
- All three angles are congruent and are equal to 60 degrees.
- It is a regular polygon with three sides.
- The perpendicular drawn from vertex of the equilateral triangle to the opposite side bisects it into equal halves. …
- The ortho-centre and centroid are at the same point.
When are triangles considered similar?
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
What are the three types of triangles?
Triangles are grouped into three kinds based on the measure of their angles:
- Acute triangle
- Obtuse triangle
- Right triangle
How to solve 45-45-90 triangles?
When given the length of the hypotenuse of a 45°-45°-90° triangle, you can calculate the side lengths by simply dividing the hypotenuse by √2. Note: Only the 45°-45°-90° triangles can be solved using the 1:1: √2 ratio method .
How do you construct an equilateral triangle?
- Adjust your drawing compass the establish the radius.
- Make a mark on the circle, anywhere you wish. …
- Without changing the compass, swing two small arcs above and below your circle point, so the arcs cross the circle.
- Relocate the drawing compass needle to one of those arcs.
- Swing the compass again to make a small arc on the circle.
What is the equivalent triangle formula?
An equilateral triangle is the one in which all three sides are equal. It is a special case of the isosceles triangle where the third side is also equal. In an equilateral triangle ABC, AB = BC = CA.
What is the meaning of equivalent triangle?
mathematics. : a triangle in which all three sides are the same length.
What is the equilateral triangle?
An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a “regular” triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal. An equilateral triangle also has three equal.
How do you find the area of an equivalent triangle?
To calculate the area of the triangle, multiply the base (one side of the equilateral triangle) and the height (the perpendicular bisector) and divide by two.
What is the example of equilateral triangle?
In geometry, an equilateral triangle is a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure….h = √3a/2.Area√3a2/4Height√3a/21 more row•Dec 26, 2020
What is equilateral triangle Class 7?
Equilateral Triangle: A triangle in which all three sides are of equal length and three angles are equal. Each angle is 60°
What are types of triangle?
Triangles can be classified into three types with respect to their interior angles which are: Acute-angled. Obtuse-angled. Right-angled.
What shape is a equilateral?
A shape is equilateral if all the sides are the same length. In geometry class, people learn about many shapes, such as triangles and squares. A square is equilateral, because all of its sides are the same length.
What are examples of equilateral?
You can know that a triangle is equilateral by measuring its sides. If they are of equal lengths, then the triangle is equilateral.
How do you solve an equilateral triangle?
0:205:25Area of an Equilateral Triangle – YouTubeYouTubeStart of suggested clipEnd of suggested clipSo s in this example is 10. So it’s the square root of 3 over 4 times 10 squared now 10 squared isMoreSo s in this example is 10. So it’s the square root of 3 over 4 times 10 squared now 10 squared is 100. And if we take 100 and divide it by four that’s twenty-five.
How do you do an equilateral triangle?
1:132:33How To Construct An Equilateral Triangle – YouTubeYouTubeStart of suggested clipEnd of suggested clipNotice that the other two sides of the equilateral triangle are the radii of two other circles withMoreNotice that the other two sides of the equilateral triangle are the radii of two other circles with its center at both endpoints. So all the sides are equal length and therefore congruent.
What is the formula of equilateral triangle height?
and the equation for the height of an equilateral triangle looks as follows: h = a × √3 / 2 , where a is a side of the triangle.
What is an equilateral triangle?
The equilateral triangle is a special case of an isosceles triangle having not just two, but all three sides equal.
How can I use the equilateral triangle calculator?
Let’s take the example from everyday life: we want to find all the parameters of the yield sign.
How to find perimeter of equilateral triangle?
The regular triangle has all sides equal, so the formula for the perimeter is: perimeter = 3 * a.
What is the hypotenuse of a right triangle?
One leg of that right triangle is equal to height, other leg is half of the side, and the hypotenuse is the equilateral triangle side. After simple transformations we get a formula for the height of the equilateral triangle:
How to find area of a triangle?
The basic formula for triangle area is side a (base) times the height h, divided by 2: area = (a * h) / 2. Height of the equilateral triangle is splitting the equilateral triangle into two right triangles. One leg of that right triangle is equal to height, other leg is half of the side, and the hypotenuse is the equilateral triangle side.
Can you calculate anything in any order?
You can calculate anything, in any order.
Equilateral Triangle Shape
A = angle A
a = side a
B = angle B
b = side b
C = angle C
c = side c
A = B = C = 60°
a = b = c
K = area
P = perimeter
s = semiperimeter
h = altitude
Calculator Use
An equilateral triangle is a special case of a triangle where all 3 sides have equal length and all 3 angles are equal to 60 degrees. The altitude shown h is h b or, the altitude of b. For equilateral triangles h = ha = hb = hc.
What is similar triangle?
Similar Triangles. Two triangles are Similar if the only difference is size (and possibly the need to turn or flip one around). These triangles are all similar: (Equal angles have been marked with the same number of arcs) Some of them have different sizes and some of them have been turned or flipped. Also notice that the corresponding sides face …
What are some examples of similar triangles?
In similar triangles, corresponding sides are always in the same ratio. For example: Triangles R and S are similar. The equal angles are marked with the same numbers of arcs.
Can we calculate lengths we don’t know yet?
We can sometimes calculate lengths we don’t know yet.
What are the names of the three types of triangles?
Equilateral, Isosceles and Scalene . There are three special names given to triangles that tell how many sides (or angles) are equal. There can be 3, 2 or no equal sides/angles:
What is the meaning of the scalene triangle?
Isosceles: means “equal legs”, and we have two legs, right? Also i SOS celes has two equal “S ides” joined by an ” O dd” side. Scalene: means “uneven” or “odd”, so no equal sides.
What Type of Angle?
Triangles can also have names that tell you what type of angle is inside:
What is equivalent in geometry?
Equivalent: this is the huge exploration that occurs in geometry. Equivalent figures are alike in some particular way, they have the same value, cover the same area, but they have different shapes.
What is the yellow triangle?
The yellow equilateral triangle must be equivalent to the green hexagon and to the grey hexagon. If the yellow equilateral triangle is equivalent to the green trapezium it must be equivalent to three equilateral triangles, so each of the three equilateral triangles must be 1/3 of the trapezium.
How many right angled isosceles triangles are there?
result is 16 right-angled isosceles triangles, each of which is one sixteenth of the whole square.
What does superimpose mean in a triangle?
Superimpose the two large triangles and show that each point, line and angle corresponds, ‘They identical in every respect, the same in every way, so lets just leave them out’.
What squares are similar in shape?
Take the 1/4 and 1/16 square, say, ‘They have the same shape, not the same value, the angles correspond, so they are similar’.
How to divide squares?
Square divided by both pairs of opposing mid-points
What is the definition of similar?
Similar: this is more difficult to define. Two geometric figures are said to be similar when they are identical in one or more aspects, such as angles in the same ratio, sides in the same ratio. They are always different sizes but they must have the same shape. This is the definition we use with the children.
What is a triangle in which all sides have equal lengths?
For example, a triangle in which all three sides have equal lengths is called an equilateral triangle while a triangle in which two sides have equal lengths is called isosceles. When none of the sides of a triangle have equal lengths, it is referred to as scalene, as depicted below.
What is a triangle with vertices?
A triangle is usually referred to by its vertices. Hence, a triangle with vertices a, b, and c is typically denoted as Δabc. Furthermore, triangles tend to be described based on the length of their sides, as well as their internal angles.
What is the circumcenter of a triangle?
The center of this circle, where all the perpendicular bisectors of each side of the triangle meet , is the circumcenter of the triangle, and is the point from which the circumradius is measured. The circumcenter of the triangle does not necessarily have to be within the triangle.
How to find the inradius of a triangle?
In a triangle, the inradius can be determined by constructing two angle bisectors to determine the incenter of the triangle. The inradius is the perpendicular distance between the incenter and one of the sides of the triangle. Any side of the triangle can be used as long as the perpendicular distance between the side and the incenter is determined, since the incenter, by definition, is equidistant from each side of the triangle.
What is the unit of an angle?
Angle Unit: degree ° radian. A triangle is a polygon that has three vertices. A vertex is a point where two or more curves, lines, or edges meet; in the case of a triangle, the three vertices are joined by three line segments called edges. A triangle is usually referred to by its vertices. Hence, a triangle with vertices a, b, …
How to find the exterior angle of a triangle?
Another way to calculate the exterior angle of a triangle is to subtract the angle of the vertex of interest from 180°. The sum of the lengths of any two sides of a triangle is always larger than the length of the third side. Pythagorean theorem: The Pythagorean theorem is a theorem specific to right triangles.
What is the longest edge of a right triangle?
The longest edge of a right triangle, which is the edge opposite the right angle, is called the hypotenuse. Any triangle that is not a right triangle is classified as an oblique triangle …
Overview
Other properties
By Euler’s inequality, the equilateral triangle has the smallest ratio R/r of the circumradius to the inradius of any triangle: specifically, R/r = 2.
The triangle of largest area of all those inscribed in a given circle is equilateral; and the triangle of smallest area of all those circumscribed around a given circle is equilateral.
The ratio of the area of the incircle to the area of an equilateral triangle, , is larger than that of an…
Characterizations
A triangle ABC that has the sides a, b, c, semiperimeter s, area T, exradii ra, rb, rc (tangent to a, b, c respectively), and where R and r are the radii of the circumcircle and incircle respectively, is equilateral if and only if any one of the statements in the following nine categories is true. Thus these are properties that are unique to equilateral triangles, and knowing that any one of them is true directly implies that we have an equilateral triangle.
Notable theorems
Morley’s trisector theorem states that, in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle.
Napoleon’s theorem states that, if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centers of those equilateral triangles themselves form an equilateral triangle.
Geometric construction
An equilateral triangle is easily constructed using a straightedge and compass, because 3 is a Fermat prime. Draw a straight line, and place the point of the compass on one end of the line, and swing an arc from that point to the other point of the line segment. Repeat with the other side of the line. Finally, connect the point where the two arcs intersect with each end of the line segment
In culture and society
Equilateral triangles have frequently appeared in man made constructions:
• The shape occurs in modern architecture such as the cross-section of the Gateway Arch.
• Its applications in flags and heraldry includes the flag of Nicaragua and the flag of the Philippines.
• It is a shape of a variety of road signs, including the yield sign.
See also
• Almost-equilateral Heronian triangle
• Isosceles triangle
• Ternary plot
• Trilinear coordinates