Credit: Wikipedia

What is a triangle?

A triangle is a polygon , a closed figure made up of three line segments. 
A triangle consists of 3 sides, 3 vertices and 3 angles. 
It is represented by symbol △.
A triangle is named using three capital alphabets, for example △ABC. 

What are the types of triangle?

On the basis of sides there are three triangles:
Equilateral △: All sides and angles equal
Isosceles △: Two sides and two angles equal
Scalene △: All sides and angles have different measure

On the basis of angle measure, there are 3 kinds of triangles
Obtuse △: The triangle in which one angle is more than 90 degrees
Acute △: The triangle in which all angles are less than 90 degrees
Right angled △: The triangle in which one angle is equal to 90 degrees. 

What is a scalene triangle?

A scalene △ is a triangle in which all sides and angles have different measures. 

So, what is the definition of a scalene triangle?
In a nutshell, a scalene △ has 
- all sides unequal
 -all angles unequal
-no line of symmetry


What is the area of a triangle?

If the given triangle is a right angled △ then area is = 1/2 x base x height

If the given △ is obtuse or acute, use heron's formula to find the area
First find the semi perimeter of the △, s = (a+b+c)/2, where a, b and c are the sides of the triangle

Area of the triangle is = square root of [s(s-a)(s-b)(s-c)]

Heron's formula can be used for scalene, isosceles and equilateral triangles. However, for equilateral triangle, the heron's formula on simplification gives (√3/4)x side²

So, when one asks 'What is the formula for the area of a triangle', there are two formula that we use depending on the type of triangle you are using. 

What is a right triangle?

A right angle △ is a triangle in which one of the angles is equal to 90 degree. 

- It may or may not have other sides equal (Isosceles right angled △ has remaining angles equal to 45 degrees each)
- It may or may not have a line of symmetry
- It follows the Pythagoras Theorem

What is a isosceles triangle?

An isosceles triangle has two sides equal. Since we known that equal sides have opposite angles equal, an isosceles triangle can also be defined as a △ with two equal sides and two equal angles. 

-Two sides are equal
- It has a line of symmetry
- Two angles are equal

What is the perimeter of a triangle?

Perimeter of a closed figure is calculated by adding the measures of all the sides. So, using the same criteria we can define the perimeter of a triangle as sum of lengths of its three sides. 

What is a unique triangle?

If a triangle can be drawn using only one way, then it is called a unique triangle. No matter how you flip or turn the triangle, the resulting new triangle is always congruent to the original triangle, which simply means that the corresponding sides and angles of the two triangle are equal. 

What is the median of a triangle?

The median of a triangle is a line segment which starts from one vertex of the triangle and falls on the line segment that joins the other two vertices and divides that line segment into two equal parts. 

What is the base of a triangle?
A triangle has three sides and any one of them can be considered as the base of the triangle. 

What is the altitude of a triangle?


The altitude of a triangle is a line segment that originates from one vertex of the triangle and falls on the base of the triangle (which joins the other two remaining vertices of the triangle) and makes an angle of 90 degrees with the base. 

What is a equilateral triangle?

An equilateral triangle is a triangle which has all sides and all angles equal.
-All sides are equal
- It has a line of symmetry
- All angles are equal 
- Area of an equilateral triangle is equal to (√3/4)x side²

What is the centroid of a triangle?

The centroid of the triangle is the vertex where all the three medians of the triangle meet. The centroid divides the medians in 2:1 which means the centroid is located 1/3 distance from each side and 2/3 distance from each vertex. 

What is a acute triangle?

An acute triangle is a triangle in which all the angles of the triangle are less than 90 degrees. For instance if a triangle has all angles equal to 60, it is an acute triangle, therefore, an equilateral triangle is an acute triangle. 

What is a congruent triangle?

A triangle is said to be congruent to a given triangle only if  the corresponding angles are equal in measure and the corresponding sides have the same lengths. 

Congruent triangles can be identified using the following five criterion:

SAS or Side-Angle-Side: Two triangle are said to be congruent as per SAS rule if the two corresponding sides of the given triangles are equal in length and the included angles are also equal in measure. 

SSS or Side-Side-Side: Two triangle are said to be congruent as per SSS rule if all the corresponding sides of the given triangles are equal in length.

ASA or Angle-Side-Angle: Two triangle are said to be congruent as per ASA rule if two corresponding angles of the triangles are equal in magnitude & the included corresponding sides are also equal in length.


AAS or Angle-Angle-Side: Two triangle are said to be congruent as per AAS rule if two of the corresponding angles of the given triangles are equal in measure and one corresponding non-included sides are also equal.

RHS or Right-angle-Hypotenuse-Side: Two right-angled triangle are said to be congruent as per RHS rule if both have equal hypotenuse & one of the corresponding shorter sides are also equal in length.


What is the hypotenuse of a triangle?

The longest side in a right angled triangle is known as its hypotenuse. 

What is a obtuse triangle?

An obtuse triangle is a triangle in which one of the angles are greater than 90 degrees and the other two angles are acute, that is, less than 90 degrees. 


What is the in-center of a triangle?

The in-center of a triangle is a vertex or intersection point where all the angle bisectors of the triangle meet.


Triangle ABC is an isosceles right triangle. What is the measure of a base angle? °

Isosceles triangle has two equal angles and the third angle is 90 degrees (Given that it is an isosceles right angled triangle). Let the measure of the angles be x


Sum of all the angles of a triangle is equal to 180 degrees

x + x+ 90° = 180°
2x = 90°
x = 45°

Therefore the measure of the base angle is 45°

What is the circumcenter of a triangle?

The circumcenter of the triangle is the point where the perpendicular bisectors of the sides of the triangle meet or intersect. 

What is the orthocenter of a triangle?

An orthocenter of a triangle is the point where the three altitudes of the triangle meet or intersect. Note that an altitude is a line segment that starts from a vertex and falls on the line segment that joins the remaining tow vertices and makes an angle of 90 degrees. 


What is the length of the hypotenuse of a right triangle whose legs have lengths of 5 and 12?

Using the Pythagoras theorem

h² = b² + p²

Hypotenuse, h = ?

Let the base be b= 5 cm

Let the perpendicular be p = 12 cm

h² = b² + p²

h² = 5² + 12²

h² = 5² + 12²

h² = 25 + 144

h² = 169

h² = 13²

h = 13 cm

Hence, the Hypotenuse is 13 cm.

What is the sum of the interior angles of a triangle?

The sum of the interior angles of a triangle is equal to 180. This is also known as the angle sum property of a triangle. 


The vertex angle of an isosceles triangle measures 40°. what is the measure of a base angle?

Isosceles triangle has two equal angles which are given to be 40° each. Let the measure of the angles be x

Sum of all the angles of a triangle is equal to 180 degrees

x + 40°+ 40° = 180°
x = 180° - 80°
x = 100°

Therefore the measure of the base angle is 100°

What is the angle of a triangle?

An angle of a triangle is the space between the two lines that meet to form a vertex, since a triangle has three vertices, there are three angles. 


What is a regular triangle?

Just like a regular polygon, in which the closed figure has all sides and angles equal or congruent,, in a regular triangle also all 3 sides have equal length and the measure of the three angles is also equal. 


What is a right isosceles triangle?

A right isosceles triangle is a triangle with 90 degrees as the base angle and the remaining two angles are acute & equal in measure. 

What is the leg of a triangle?

The legs of the triangle are the sides in the right angled triangle that form the 90 degree angle (i.e. base and perpendicular); the third side is known as hypotenuse. 

What is a triangle with two equal sides?

Isosceles triangle is the triangle that has two equal sides. 

What is the total angle of a triangle?

The sum of all the interior angles of a triangle sums up to give 180 degrees. 


What is the midsegment of a triangle?

Make a line segment by joining the midpoints of the two sides of the triangle. This line segment so formed, parallel to the third side is known as the midsegment of the triangle. 

 
What is the exterior angle of a triangle?

When one side of a triangle is extended, a non-straight angle adjacent to one interior angle is formed. This is known as the exterior angle of the triangle. 
The sum of all the exterior angles of a triangle add up to give a sum of 180 degrees. 

The sides of a triangle are in the ratio 3:4:5 what is the length of each side?

Let the sides of the triangle be 3x, 4x and 5x.

Since (5x)² = (3x)² + (4x)², that means it follows Pythagoras theorem and it is a right angled triangle. 

Using Pythagorean triplets

m²-1, 2m, m²+1

Let 2m = 4x
m = 2x

Let m² -1 = 3x
(2x)² - 1 = 3x
4x² - 3x - 1 = 0
4x² - 4x + x -1 = 0
4x (x-1) +1 (x-1) = 0

x=1, x = 1/4

Taking x =1
So the length of the sides are 3 units, 4 units and 5 units.

What is the degrees of a triangle? (or, what degrees is a triangle)

The sum of all interior and exterior angle of a triangle is equal to 180 degrees respectively. 

How many acute angles are in a right triangle?
In a right angled triangle there are two acute angles. 

What is the vertex of a triangle?

The vertex of a triangle is a point where the sides of the meet. A triangle has 3 vertices. 

What is a right scalene triangle?

A right scalene triangle has no sides equal but follows the Pythagoras theorem and has one angle equal to 90 degrees. 

What is a triangle with no congruent sides?

A triangle with no congruent sides is known as scalene triangle.


What is the point of concurrency of the medians of a triangle?

what is the point of concurrency of the medians of a triangle is known as centroid. 

What is a 3d triangle called?

A 3D triangle is known as tetrahedron which is made up of four equilateral triangles. 


What is a triangle with no equal sides?

A triangle with no equal sides is known as scalene triangle. 

What is the sum of the exterior angles of a triangle?

The sum of the exterior angles of a triangle is 180 degrees. 

What is the least number of acute angles that a triangle can have?

The least number of acute angles that a triangle can have is two. 

What is the volume of a triangle?

A triangle is a 2-D structure, it does not have a volume. 

What is a perpendicular bisector of a triangle?
A perpendicular bisector of a triangle is a line segment that starts from a vertex and falls on the opposite side and divides its into two equal parts. It also makes an angle of 90 degrees with the line segment on which it falls. 

What is the length of a triangle?

The length of a triangle is its perimeter, which is equal to sum of the lengths of its 3 sides. 


What is a 30 60 90 triangle?

A 30-60-90 triangle is a special right angled triangle in which the two angles other than the right angle are of measure 30 and 60 degrees. 

 
What is the longest side of a right triangle?
Hypotenuse is the longest side of a right angled triangle. 

What is a 3:4:5 triangle?

A 3:4:5 triangle is the one in which either the 3 sides or the 3 angles are in 3:4:5 ratio. 

What is the greatest number of acute angles that a triangle can contain?

A triangle can contain maximum three acute angles, for example equilateral triangle. 

What is the perimeter of a right triangle?

The perimeter of a right angled triangle can be calculated by adding the lengths of its three sides.