Mixed Deck — All Geometry Topics Flashcards

What is the coordinate plane?

Answer: A two-dimensional surface with x and y axes

The coordinate plane is a fundamental tool in geometry, consisting of two perpendicular number lines: the horizontal x-axis and the vertical y-axis, intersecting at the origin (0,0). It provides a system for precisely locating points and graphing equations in two dimensions.

What is a triangle?

Answer: A polygon with three sides and three vertices

A triangle is a fundamental polygon defined by three sides and three vertices (corners). It is the simplest polygon and its interior angles always sum to 180 degrees. Triangles are extensively used in geometry, engineering, and architecture due to their rigidity and versatility.

To construct a regular hexagon inscribed in a circle, you:

Answer: Set the compass to the circle's radius and step off six equal arcs around the circle

The radius of a circle equals the side length of the inscribed regular hexagon, so stepping the compass radius around the circle marks six equally spaced points.

In a 30-60-90 triangle, if the shortest side is 5, what is the hypotenuse?

Answer: 10

The hypotenuse is twice the shortest side, so 2 × 5 = 10.

Which solid has one circular base and a single vertex (apex)?

Answer: Cone

A cone has one circular base narrowing to a single apex.

In a circle of radius 10, a sector has area 25π. What is its central angle?

Answer: 90°

25π = (θ/360)π(100), so θ/360 = 1/4, giving θ = 90°.

Which quadrilateral has exactly one pair of parallel sides?

Answer: Trapezoid

A trapezoid is defined by having exactly one pair of parallel sides.

A cube has a side length of 4 cm. What is its volume?

Answer: 64 cm³

The volume of a cube is s³, so 4³ = 64 cm³.

What does sin(2θ) equal by the double-angle formula?

Answer: 2 sin θ cos θ

The double-angle formula gives sin 2θ = 2 sin θ cos θ.

If a photo is enlarged so each side triples, the new area compared to the original is:

Answer: 9 times larger

Area scales by 3² = 9 times.

A trapezoid has parallel sides of 8 and 12 and a height of 5. What is its area?

Answer: 50

Area = ½(b₁ + b₂)·h = ½(8 + 12)(5) = 50.

Line l is parallel to line m. A transversal creates an angle of 72° with line l. What is the corresponding angle with line m?

Answer: 72°

Corresponding angles are congruent when lines are parallel, so the angle with line m is also 72°.

Which function is used to find an angle given two sides?

Answer: Inverse functions like sin⁻¹

When you know the ratio of two sides in a right triangle (e.g., opposite/hypotenuse for sine), you use inverse trigonometric functions (arcsin, arccos, arctan) to find the measure of the angle itself. For example, if sin(θ) = 0.5, then θ = sin⁻¹(0.5) = 30 degrees. These functions essentially "undo" the regular trigonometric functions.

What is the Pythagorean identity?

Answer: sin²θ + cos²θ = 1

The Pythagorean identity, sin²θ + cos²θ = 1, is a fundamental trigonometric identity derived directly from the Pythagorean theorem and the definitions of sine and cosine in a right triangle. It holds true for any angle θ and is widely used to simplify trigonometric expressions and solve equations.

Two parallel lines are cut by a transversal forming co-interior angles of 3x° and (2x + 10)°. What is x?

Answer: 34

Co-interior angles sum to 180°: 3x + 2x + 10 = 180, so 5x = 170 and x = 34.

How many edges does a triangular prism have?

Answer: 9

A triangular prism has 9 edges: 3 on each triangular base and 3 lateral edges connecting them.

A cylinder has a base radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)

Answer: 282.6 cm³

Cylinder volume is πr²h = 3.14 × 9 × 10 = 282.6 cm³.

A line parallel to one side of a triangle divides the other two sides proportionally. This is known as the:

Answer: Triangle Proportionality Theorem

The Triangle Proportionality (Basic Proportionality) Theorem states a parallel line cuts the sides proportionally.

What is the area of a triangle with base 10 and height 6?

Answer: 30

Area = ½·base·height = ½(10)(6) = 30.

What is the total measure of a straight angle?

Answer: 180 degrees

A straight angle is an angle that measures exactly 180 degrees. When two rays form a straight angle, they point in opposite directions, creating a straight line. It essentially represents half of a full rotation.