Triangle Rigidity & Classification
What are the three ways to classify triangles by their angles?
Acute, right, obtuse
What does the Triangle Inequality Theorem state?
The sum of any two side lengths of a triangle must be greater than the third side.
What is the sum of the three interior angles of any triangle?
180°
What is an exterior angle of a triangle?
An angle formed by extending one side of a triangle.
Can a triangle have two right angles? Explain.
No. Two right angles total 180°, leaving 0° for the third angle.
What does it mean for a geometric figure to be rigid?
It cannot change shape without changing its side lengths. (distorted under stress)
Can side lengths 3, 4, and 8 form a triangle?
No, because 3 + 4 < 8.
A triangle has angles measuring 50° and 70°. What is the third angle?
60°
An exterior angle measures 120°. What is the measure of its adjacent interior angle?
60°
A triangle has angles measuring 40°, 60°, and 80°. Classify the triangle by its angles.
Acute triangle
A triangle has angles measuring 35°, 55°, and 90°. Classify the triangle by its angles.
Right triangle
Can side lengths 6, 9, and 12 form a triangle? Explain.
Yes, because 6 + 9 > 12.
A right triangle has one acute angle measuring 37°. What is the other acute angle?
53°
Two remote interior angles measure 45° and 65°. What is the exterior angle?
110°
A triangle has side lengths 7, 10, and x. What is the smallest possible integer value of x? (whole number)
4
Why are triangles commonly used in bridges and building structures instead of squares?
Triangles are rigid and resist changing shape.
Two sides of a triangle measure 5 and 11. What is the possible range for the third side, x?
6 < x < 16
The three angles of a triangle measure x°, 2x°, and 3x°. Find x.
x = 30
An exterior angle measures 135°. One remote interior angle measures 55°. What is the other remote interior angle?
80°
An exterior angle measures 125°, and one remote interior angle measures 75°. Find the other remote interior angle and the adjacent interior angle.
Remote interior = 50°; adjacent interior = 55°.
A square frame can change shape without changing its side lengths. What could you add to make the square rigid, and why?
Add a diagonal to create two rigid triangles.
Two sides of a triangle measure 8 and 13. What are all possible integer values for the third side?
6 through 20
The angles of a triangle measure (2x+10)°, (3x−5)°, and (x+25)°. Find x and all three angle measures.
x = 25; angles are 60°, 70°, and 50°.
An exterior angle measures (5x + 10)°. Its remote interior angles measure (2x + 20)° and (x + 30)°. Find x and the exterior angle.
x = 20; exterior angle = 110°.
A triangle has interior angles measuring (2x+10)°, (3x−20)°, and (x+10)°. Find x and the measure of the exterior angle adjacent to the largest interior angle.
x = 30; interior angles are 70°, 70°, and 40°. Exterior angle = 110°.