Geometry and Trigonometry Concepts

These flashcards cover essential vocabulary and definitions related to geometry and trigonometry as presented in the lecture notes.

Vertically Opposite Angles

Angles that are opposite each other when two lines intersect; they are equal.

Alternate Angles

Angles that are on opposite sides of a transversal but inside two parallel lines; they are equal.

Corresponding Angles

Angles that are in the same position on two parallel lines in relation to a transversal; they are equal.

Interior Angles

The angles formed inside a polygon; in a triangle, they add up to 180°.

Quadrilateral Angles

The sum of the interior angles in a quadrilateral is 360°.

Right Triangle

A triangle that has one angle equal to 90°.

Equilateral Triangle

A triangle in which all three sides and angles are equal.

Scalene Triangle

A triangle in which all three sides and angles are different.

Area of Triangle

Area (A) = ½ (base × height).

Area of Rectangle

Area (A) = width × length.

Area of Square

Area (A) = side².

Area of Parallelogram

Area (A) = base × height.

Area of Kite

Area (A) = (d₁ × d₂) / 2, where d₁ and d₂ are the diagonals.

Area of Trapezoid

Area (A) = ½ (a + b) × height, where a and b are the lengths of the two bases.

Trigonometry

The study of relationships between the angles and sides of right-angled triangles.

Hypotenuse

The longest side of a right triangle, opposite the right angle.

Opposite Side

The side opposite to the angle of interest in a right triangle.

Adjacent Side

The side next to the angle of interest in a right triangle.

Sine (sin)

The ratio of the length of the opposite side to the hypotenuse in a right triangle.

Cosine (cos)

The ratio of the length of the adjacent side to the hypotenuse in a right triangle.

Tangent (tan)

The ratio of the length of the opposite side to the adjacent side in a right triangle.

Trigonometric Ratios Ex 1

In a right triangle, if AB is the hypotenuse, CB is adjacent, and AC is opposite.

Finding Unknown Angles

Use calculator functions SHIFT + sin, SHIFT + cos, or SHIFT + tan to find unknown angles.