Triangle Fundamentals

30 question-and-answer flashcards that review definitions, classifications, angle relationships, and key theorems about triangles from the lecture.

What is a triangle?

A polygon composed of three line segments (sides) that meet at three points (vertices).

What is another term for a triangle?

Trilateral.

How many sides does every triangle have?

Three.

What two main criteria are used to classify triangles?

By their sides and by their angles.

Name the three classifications of triangles by side length.

Scalene, Isosceles, and Equilateral.

What is a scalene triangle?

A triangle with all three sides of different lengths (and all angles different).

What is an isosceles triangle?

A triangle with exactly two equal sides and two equal angles.

What is an equilateral triangle?

A triangle with all three sides equal; it is also equiangular.

List the four angle-based classifications of triangles.

Acute, Right, Obtuse, and Equiangular.

What defines an acute triangle?

All three interior angles are less than 90°.

What defines a right triangle?

One interior angle measures exactly 90°.

What defines an obtuse triangle?

One interior angle is greater than 90° but less than 180°.

What defines an equiangular triangle?

All three interior angles are congruent, each measuring 60°.

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

180°.

What theorem states that the interior angles of a triangle sum to 180°?

The Triangle Sum Theorem.

What is an exterior angle of a triangle?

An angle formed by extending one side of the triangle beyond a vertex.

State the Exterior Angle Theorem.

The measure of an exterior angle equals the sum of the two non-adjacent (remote) interior angles.

What are remote interior angles?

The two interior angles of a triangle that are not adjacent to a given exterior angle.

In triangle terminology, what is a vertex?

The point where two sides meet.

What are the adjacent sides of an angle in a triangle?

The two sides that form that angle.

What is the side opposite a given angle in a triangle?

The side that does not form the angle.

In a right triangle, what is the hypotenuse?

The longest side, opposite the right angle.

What are the legs of a right triangle?

The two sides that form the right angle.

In an isosceles triangle, what is the base?

The side that is not congruent to the other two equal sides.

State the Pythagorean Theorem.

For a right triangle, a² + b² = c², where c is the hypotenuse.

What are complementary angles?

Two angles whose measures add up to 90°.

What are supplementary angles?

Two angles whose measures add up to 180°.

What is the relationship between the two acute angles of a right triangle?

They are complementary (their measures add to 90°).

How would you classify a triangle with side lengths 5 cm, 6 cm, and 7 cm?

Scalene triangle (all sides unequal).

How would you classify a triangle with two equal sides and one obtuse angle?

Obtuse Isosceles triangle.