MathIsimple

Triangles Beginner

Master triangle fundamentals: definitions, classification by sides and angles, the angle sum theorem, triangle inequalities, and multiple area formulas—all in one comprehensive lesson.

Geometry
Beginner
~60 min
Triangle Calculator
Calculate area using base-height, Heron's formula, or SAS method
Triangle Area Calculator

Calculate triangle area using multiple mathematical methods. Choose the method based on your known values.

Calculation Method

Calculation Method:

Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
Results
1. What is a Triangle?

A triangle is a polygon with exactly three vertices, three sides, and three interior angles. It is the simplest closed figure you can create with straight lines.

Standard Notation

  • Vertices: A, B, C (uppercase letters)
  • Sides: a, b, c (lowercase, opposite to corresponding vertex)
  • Angles: ∠A, ∠B, ∠C (at each vertex)
  • Triangle: △ABC

Key Convention

Side aa is opposite vertex A (connecting vertices B and C). This naming convention is used throughout geometry and trigonometry.

Why Triangles Are Rigid

If you fix the lengths of all three sides, the triangle's shape is completely determined. Unlike quadrilaterals (which can flex), triangles cannot deform without breaking a side. This is why triangles appear everywhere in construction: roof trusses, bridges, bicycle frames.

2. Classification by Sides and Angles
3. Angle Sum Theorem
4. Triangle Inequality
5. Triangle Area Formulas

Practice Quiz

Practice Quiz
20
Questions
0
Correct
0%
Accuracy
1
What is the sum of interior angles in any triangle?
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2
If two angles of a triangle are 50°50° and 60°60°, what is the third angle?
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3
A triangle with all sides equal is called:
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4
Which triangle has exactly one angle of 90°90°?
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5
Can a triangle have sides of lengths 2, 3, and 7?
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6
The area of a triangle with base 10 and height 6 is:
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7
An isosceles triangle has base angles of 70°70° each. What is the vertex angle?
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8
Which formula calculates triangle area using only the three side lengths?
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9
A triangle with sides 3, 4, 5 is:
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10
What is the exterior angle at vertex A if the interior angle at A is 50°50°?
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11
In a triangle, the longest side is always opposite to:
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12
A triangle with all angles less than 90°90° is called:
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13
What is the area of an equilateral triangle with side length 4?
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14
If a triangle has angles xx, 2x2x, and 3x3x, what is xx?
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15
Which of these is NOT a valid triangle?
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16
The exterior angle of a triangle equals:
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17
A scalene triangle has:
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18
In a right triangle with legs 6 and 8, what is the area?
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19
Why are triangles used in construction and engineering?
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20
Can a triangle have two obtuse angles?
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