Geometry: Shapes, Theorems & Formulas
A focused review of high school Geometry, covering 44 core definitions, theorems, and formulas. Topics include points, lines, and angles; angle relationships formed by parallel lines and transversals; triangle classifications and the Pythagorean Theorem; area, perimeter, and circumference formulas for common shapes; circle terminology; volume and surface area formulas for solids; and congruence versus similarity. Great for exam prep or reinforcing spatial reasoning fundamentals.
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#1
Q:What is a point?
- A:A location in space with no size, dimension, or shape.
#2
Q:What is a line?
- A:A straight path of points that extends infinitely in both directions.
#3
Q:What is a line segment?
- A:A part of a line with two defined endpoints.
#4
Q:What is a ray?
- A:A part of a line with one endpoint that extends infinitely in one direction.
#5
Q:What is a plane?
- A:A flat, two-dimensional surface that extends infinitely in all directions.
#6
Q:What is an angle?
- A:The figure formed by two rays that share a common endpoint, called the vertex.
#7
Q:What is an acute angle?
- A:An angle measuring less than 90°.
#8
Q:What is a right angle?
- A:An angle measuring exactly 90°.
#9
Q:What is an obtuse angle?
- A:An angle measuring more than 90° but less than 180°.
#10
Q:What is a straight angle?
- A:An angle measuring exactly 180°.
#11
Q:What are complementary angles?
- A:Two angles whose measures add up to 90°.
#12
Q:What are supplementary angles?
- A:Two angles whose measures add up to 180°.
#13
Q:What are vertical angles?
- A:A pair of opposite angles formed by two intersecting lines; they are always equal.
#14
Q:What are corresponding angles?
- A:Angles in matching positions when a transversal crosses two lines; equal if the lines are parallel.
#15
Q:What are alternate interior angles?
- A:Angles on opposite sides of a transversal, between the two lines; equal if the lines are parallel.
#16
Q:What is the sum of the interior angles of a triangle?
- A:180°
#17
Q:What is an equilateral triangle?
- A:A triangle with three equal sides and three 60° angles.
#18
Q:What is an isosceles triangle?
- A:A triangle with two equal sides and two equal angles.
#19
Q:What is a scalene triangle?
- A:A triangle with no equal sides or equal angles.
#20
Q:What is a right triangle?
- A:A triangle that has one 90° angle.
#21
Q:What is the Pythagorean Theorem?
- A:a² + b² = c², where c is the hypotenuse of a right triangle.
#22
Q:What is a common Pythagorean triple?
- A:3, 4, 5 (since 3² + 4² = 5²)
#23
Q:What is the formula for the area of a triangle?
- A:A = ½ × base × height
#24
Q:What is the formula for the area of a rectangle?
- A:A = length × width
#25
Q:What is the formula for the area of a square?
- A:A = side²
#26
Q:What is the formula for the area of a parallelogram?
- A:A = base × height
#27
Q:What is the formula for the area of a trapezoid?
- A:A = ½ × (base1 + base2) × height
#28
Q:What is the formula for the area of a circle?
- A:A = πr²
#29
Q:What is the formula for the circumference of a circle?
- A:C = 2πr (or πd)
#30
Q:What is the formula for the sum of the interior angles of a polygon with n sides?
- A:(n - 2) × 180°
#31
Q:What is the sum of the exterior angles of any convex polygon?
- A:360°
#32
Q:What is a regular polygon?
- A:A polygon with all sides equal in length and all angles equal in measure.
#33
Q:What is the radius of a circle?
- A:The distance from the center of the circle to any point on it.
#34
Q:What is the diameter of a circle?
- A:A line segment through the center connecting two points on the circle; it equals twice the radius.
#35
Q:What is a chord of a circle?
- A:A line segment connecting two points on the circle.
#36
Q:What is a tangent to a circle?
- A:A line that touches the circle at exactly one point.
#37
Q:What is an arc of a circle?
- A:A portion of the circle's circumference.
#38
Q:What is the formula for the volume of a rectangular prism?
- A:V = length × width × height
#39
Q:What is the formula for the volume of a cube?
- A:V = side³
#40
Q:What is the formula for the volume of a cylinder?
- A:V = πr²h
#41
Q:What is the formula for the volume of a sphere?
- A:V = (4/3)πr³
#42
Q:What is the formula for the volume of a cone?
- A:V = (1/3)πr²h
#43
Q:What is the formula for the surface area of a sphere?
- A:SA = 4πr²
#44
Q:What does it mean for two figures to be congruent?
- A:They have exactly the same size and shape.
#45
Q:What does it mean for two figures to be similar?
- A:They have the same shape but different sizes, with proportional sides and equal angles.