ABC is an equilateral triangle with point D on side BC such that BD = BC/3 . Let E be a point on the side of BC such that AE⊥BC.

How do you make an equilateral triangle?

To trisect the original triangle, we need Divide the larger triangle (AIC) into two equal triangles. This can be done by finding the midpoints of any sides of the triangle and constructing line segments from them to the opposite vertices. Both possibilities can be seen below.

How to prove that triangle ABC is an equilateral triangle?

We know that all sides of an equilateral triangle are equal, which means that in triangle ABC, we have AB = BC = AC. We know that the opposite angles of an equilateral triangle are equal. So, here we have side AB equal to side AC, which means ∠B=∠C…

Are all angles of an equilateral triangle the same?

Sal proves that the interior angles of an equilateral triangle are exactly the same (so they both measure 60°) Conversely, a triangle with all congruent angles is equilateral.

What are the sides of an equilateral triangle

In geometry, an equilateral triangle is a triangle where All three sides are the same length. In familiar Euclidean geometry, equilateral triangles are also equiangular. That is, all three interior angles are also congruent to each other at 60°.

In an equilateral triangle ABC, D is a point on the side of BC such that BD = 1/3 BC. prove..

37 related questions found

What is the shortest side of a 30 60 90 triangle?

And since we know we cut the base of an equilateral triangle in half, we can see that the opposite side of the 30° angle (shortest side) of each of our 30-60-90 triangles is exactly half the length of the hypotenuse.

Why is the area of ​​an equilateral triangle

In general, the height of an equilateral triangle is equal to √3/2 times the length of the side of the equilateral triangle.The area of ​​an equilateral triangle is equal to 1/2 * √3s/ 2 * s = √3s2/4.

What is the angle between two equilateral sides?

In an equilateral triangle, all sides are equal and all angles are equal 60°. In an isosceles triangle, the two sides are the same length, and the two angles (the ones formed with the base line) are equal.

What is the side length of an equilateral triangle?

An equilateral triangle is a special case of a triangle, where All 3 sides are of equal length And all 3 angles are equal to 60 degrees.

What does an equilateral triangle look like?

An equilateral triangle is a three-sided polygon (closed shape) whose sides are congruent (equal length). An equilateral triangle also has 3 congruent angles, all of which are 60°.

What is the sum of equilateral triangles?

The sum of all interior angles of an equilateral triangle is equal to 180 degrees.

Is an equilateral triangle equiangular?

Every equilateral triangle is also an isosceles triangle, so any two sides that are equal have equal opposite angles. Therefore, since all three sides of an equilateral triangle are equal, all three angles are also equal.Therefore, every equilateral triangle also isometric.

What are the five steps in constructing an equilateral triangle?

• Step 1: Mark point B on the line.
• Step 2: Stretch the compass to any width. Place the tip of the compass at point B and draw an arc on the line. Mark the point where the arc meets the line as point C.
• Step 5: Draw a line from point B to the intersection of the two arcs. Mark the angle 60°.

How to draw a 6 cm equilateral triangle?

Construct an equilateral triangle with sides 6 cm long.

1. Draw BC = 6 cm.
2. With B as the center and 6cm as the radius, draw an arc on one side of BC.
3. Taking C as ccntre and 6 cm as radius, draw another arc on the same side of BC and intersect the previous arc at A.
4. Combine AB and AC.

How many attitudes does an equilateral triangle have?

Equilateral triangle has three consistent sidesIt is also an equilateral triangle with three congruent angles, each of which is 60 degrees.

What is the formula for calculating an equilateral triangle?

The formula for the area of ​​an equilateral triangle is equal to 3/4 times the square of the side length of an equilateral triangle.

What is the area formula?

Given a rectangle of length l and width w, the formula for area is: A = lw(rectangle).That is, the area of ​​the rectangle is length times width. As a special case, since in the case of a square l = w, the area of ​​a square of side length s is given by the formula: A = s2(square).

How do you find a 30-60-90 triangle?

30-60-90 Triangle Ratio

1. Short side (opposite of 30 degree angle) = x.
2. hypotenuse (opposite of 90 degree angle) = 2x.
3. Long side (opposite of 60 degree angle) = x√3.

How can I tell if it’s a 30-60-90 triangle?

In any 30-60-90 triangle, you’ll see the following: The shortest leg is opposite the 30 degree anglethe length of the hypotenuse is always twice the length of the shortest leg, you can find the length of the long leg by multiplying the short leg by the square root of 3.

What is an example of an equilateral triangle?

An equilateral triangle is a type of triangle. It is a regular polygon with special properties: the lengths of the three sides are equal, and the angles of the three corners are all 60º.Real life examples can include Traffic signs, pizza slices and nachos.

What is an example of an equilateral triangle?

In geometry, an equilateral triangle is A triangle with three sides of equal length…we can find the triangular shape in the pool stands, roadside signs and a piece of pizza all around us.