Geometry Theorems and Concepts

This video tutorial by Ben covers multiple-choice questions from the January 2023 geometry regions exam. It includes explanations on reflections, rotations, circle rotations, side splitter theorem, trigonometry in right triangles, angle bisectors, altitudes, cost calculations, Pythagorean triples, similar triangles, quadrilateral properties, circle volume calculations, rotational symmetry, and dilation effects on lines.

Which transformation preserves both distance and angles in a triangle?

• Shear

• Translation

• Dilation

• Reflection

What is the three-dimensional object formed when a circle is rotated about its diameter?

• Cylinder

• Cone

• Torus

• Sphere

In a triangle, if a line parallel to one side divides the other two sides proportionally, which theorem is being applied?

• Pythagorean Theorem

• Midsegment Theorem

• Side Splitter Theorem

• Angle Bisector Theorem

What is the relationship between sine and cosine for complementary angles in a right triangle?

• They are cofunctions

• They are inverses

• They are reciprocals

• They are equal

How do you calculate the cost of materials given the volume, density, and price per unit weight?

• Multiply volume by price and divide by density

• Add volume, density, and price

• Multiply volume by density and price

• Divide volume by density and multiply by price

Which quadrilateral does not always have congruent diagonals?

• Isosceles Trapezoid

• Rhombus

• Rectangle

• Square

What is the formula for the volume of a sphere?

• 2πr

• πr^2h

• 4/3 πr^3

• 1/3 πr^2h

What is the minimum rotation angle for a rectangle to map onto itself?

• 360 degrees

• 270 degrees

• 180 degrees

• 90 degrees

What is the relationship between the diagonals of a parallelogram if they bisect each other?

• They are parallel

• They bisect each other

• They are congruent

• They are perpendicular

How do you determine the area of a sector in a circle?

• θ/360 × πr^2

• 2πr

• πr^2

• 1/2 πr^2