Scenario: Construction Engineering - Learn about triangle properties through building and structural design!
You're designing a triangular roof truss for a house. The truss must be strong and stable. You need to determine the angles and classify the triangle type to ensure proper structural support.
Design Challenge:
A triangular truss has angles of 60°, 60°, and 60°. What type of triangle is this, and what are its properties?
Equilateral triangle - all sides equal, all angles equal to 60°
All three sides are equal
All angles = 60°
Two sides are equal
Two angles are equal
All sides are different
All angles are different
All angles < 90°
Example: 60°, 60°, 60°
One angle = 90°
Example: 30°, 60°, 90°
One angle > 90°
Example: 20°, 30°, 130°
Triangle Angle Sum Theorem: The sum of the interior angles of any triangle is always 180°.
This is true for ALL triangles, regardless of their size or shape.
A construction worker needs to build a triangular support beam. Two angles are 45° and 60°. What is the measure of the third angle?
Given: Two angles are 45° and 60°
Step 1: Add the known angles
45° + 60° = 105°
Step 2: Subtract from 180°
180° - 105° = 75°
Answer: The third angle is 75°
Triangle Inequality Theorem: The sum of any two sides of a triangle must be greater than the third side.
This means: a + b > c, a + c > b, and b + c > a
An engineer is designing a triangular bridge support. Can a triangle be formed with sides of 5 ft, 8 ft, and 15 ft?
Check 1: 5 + 8 = 13, 13 > 15? No!
Check 2: 5 + 15 = 20, 20 > 8? Yes!
Check 3: 8 + 15 = 23, 23 > 5? Yes!
Answer: No, this triangle cannot be formed because 5 + 8 = 13 < 15
A triangle has angles of 30° and 80°. Find the third angle and classify the triangle by angles.
Your solution:
Classify a triangle with sides of 6 cm, 6 cm, and 8 cm by both sides and angles.
Your answer: