What are the three key components that define a triangle?

The three key components that define a triangle are vertices, sides, and angles.

Vertices of a triangle are defined as ___.

The three corner points where the lines meet.

True or False: The order of vertices when naming a triangle affects its identity.

False. The order of the vertices does not matter; ∆ABC is the same as ∆BCA, ∆CAB, etc.

What is the defining characteristic of an equilateral triangle?

An equilateral triangle has all three sides of equal length, and consequently, all three angles also measure 60 degrees.

True or False: A triangle can be formed by connecting three collinear points.

False. If three points are collinear, connecting them only forms a line segment, not a triangle.

The line segment drawn from a triangle's vertex perpendicular to the opposite side is called an ___.

Altitude

A triangle has sides 6 cm, 7 cm, and 14 cm. Can it exist?

No
 6 + 7 = 13 < 14 → Violates Triangle Inequality Theorem.

Which of the following can be both isosceles and right-angled?
a) A triangle with angles 90°, 45°, 45°
b) A triangle with sides 3 cm, 3 cm, 3 cm
c) A triangle with angles 30°, 60°, 90°

a) 90°, 45°, 45° triangle has two equal angles and one right angle → Isosceles and right-angled.

Why can’t a triangle have two right angles?

Because the sum of angles in any triangle is 180°, and two right angles would already sum to 180°, leaving no space for the third angle.

I’m a triangle with one angle at 125°. What’s my angle-based name?

125°> 90° 

 → obtuse-angled triangle

True or False: The exterior angle of a triangle equals the sum of the two opposite interior angles.

True