# Can we construct equilateral triangle?

## Can we construct equilateral triangle?

An equilateral triangle is one with all three sides the same length. It begins with a given line segment which is the length of each side of the desired equilateral triangle. It works because the compass width is not changed between drawing each side, guaranteeing they are all congruent (same length).

### How do you justify in construction class 9?

Justification of Construction: We can justify the construction by showing ABC as an equilateral triangle i.e., AB = BC = AC = 5 cm and ∠A = ∠B = ∠C = 60°. In ΔABC, we have AC = AB = 5 cm and ∠A = 60°. From equations (1) and (2), ΔABC is an equilateral triangle.

#### How do you construct a triangle in Class 10?

Case 1

1. Step 1: Construct a triangle ABC as given below:
2. Step 2: Draw a ray BX making an acute acute with the base BC and mark 5 points B1, B2, B3, B4, B5 on BX such that BB1 = B1B2 = B2B3 = B3B4 = B4B5.
3. Step 3: Join B3C and draw a line B5C’ such that B3C is parallel to B5C’, where C’ lies on the produced BC.

How do you construct an equilateral triangle with side 4.5 cm?

1. Step 1: Draw a line segment AB of length 4. 5 cms.
2. Step 2: Take 4. 5 cms as radius and A as center, draw an arc.
3. Step 3: Take 4.
4. Step 4: Let C be the point where the two arcs intersect, join AC and BC and label the sides.
5. Thus, triangle ABC is the required equilateral triangle.
6. Since all sides are equal.

How do you construct an equilateral triangle with the perimeter of 15cm?

Answer: draw a base of 5 cm and from one end make angle of 60 degree And cut an arc of 5 cm on this angle”s extended arm now from another end draw an Arc of 5 cm again ,,join the point of intersection of extended arm and the another end ,,this will be the third side of triangle .

## What is math construction?

“Construction” in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil. This is the “pure” form of geometric construction: no numbers involved!

### What are the steps in constructing construction?

Steps of construction:

1. Take point O and draw a circle of radius 4 cm.
2. Take any point P out side the circle.
3. Through the external point P draw a straight line PBA meet the given circle at A and B.
4. With AP as diameter , draw a semicircle.
5. Draw BC ⊥ AP, which intersects the semicircle at C.

#### How do you construct an equilateral triangle in a square?

How to Make an Equilateral Triangle From a Square

2. Step 2: Fold in Half. Fold the square in half hamburger/hot dog style and then unfold.
3. Step 3: Left Corner to Center.
4. Step 4: Make Two More Sides of the Triangle.
5. Step 5: Crease, Lick, Rip, Repeat.
6. Step 6: The Triangle Is Finished.

What are the steps in writing class 10 construction?

Steps of Construction:

1. Draw a circle with centre O.
2. Join the centre O to the given external point P.
3. Draw a right bisector of OP to intersect OP at Q.
4. Taking Q as the centre and OQ = PQ as radius, draw a circle to intersect the given circle at T and T’.
5. Join PT and PT’ to get the required tangents as PT and PT’.

What is the formula for an equilateral triangle?

Area of an equilateral triangle,A = (√3/4)a 2

• Perimeter of an equilateral triangle,P = 3a
• Semi perimeter of an equilateral triangle = 3a/2
• Height of an equilateral triangle,h = (√3/2)a
• ## How do you solve an equilateral triangle?

Identify angle C. It is the angle whose measure you know.

• Identify a and b as the sides that are not across from angle C.
• Substitute the values into the Law of Cosines.
• Solve the equation for the missing side.
• ### What are the three angles in an equilateral triangle?

By definition,the measure of an acute angle is less than 90 ∘.

• The sum of the interior angles of any triangle must be 180 ∘.
• Equilateral triangles have three equal sides and three equal interior angles.
• Quora is not a “magic homework machine”.
• #### What are the identifying features of an equilateral triangle?

The altitude,median,angle bisector,and perpendicular bisector for each side are all the same single line.

• These 3 lines (one for each side) are also the lines of symmetry of the triangle.
• All three of the lines mentioned above have the same length of s 3 2\\frac {s\\sqrt {3}} {2} 2s 3 ​ ​ .