Geometry Practice & Interactive Quizzes

Interactive geometry practice drills and quizzes with step-by-step answers. Master angles, area, perimeter, volume, and shapes with clear visual models.

52 practice topics available

Angles Practice

Classify angles by measure (acute, right, obtuse, straight) and calculate unknown angles using complementary (90°), supplementary (180°), and vertical angle relationships.

Area of Circles from Diameter Practice

Calculate the area of a circle when given its diameter by first finding the radius (r = d ÷ 2) and applying A = πr².

Area & Circumference of Circles

Apply the formulas for circumference (C = 2πr = πd) and area (A = πr²) of circles, converting between radius and diameter, using π ≈ 3.14.

Area of Composite Rectilinear Shapes Practice

Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts.

Area by Counting Unit Squares Practice

Measure area by counting unit squares (square cm, square m, square in, or square units) covering standard and irregular rectilinear plane figures.

Area of Circles from Radius Practice

Calculate the area of a circle given its radius using the formula Area = πr² (with π ≈ 3.14), squaring the radius before multiplying by π.

Area of Parallelograms Practice

Calculate the area of parallelograms using base and perpendicular height (A = b × h), distinguishing perpendicular height from slanted side length.

Area of Squares Practice

Calculate the area of a square by squaring its side length (A = s × s = s²), and determine the side length from a known square area.

Area of Trapezoids Practice

Calculate the area of trapezoids by averaging the parallel bases and multiplying by perpendicular height: Area = ½ × (a + b) × h.

Area of Triangles Practice

Calculate the area of right, acute, and obtuse triangles using the formula Area = (1/2) × base × height, identifying perpendicular heights correctly.

Area of Rectangles Practice

Calculate the area of rectangles by multiplying length by width (A = l × w), and find missing side lengths given total area.

Area of Rhombuses & Kites Practice

Calculate the area of rhombuses and kites using the lengths of their perpendicular diagonals: Area = ½ × d₁ × d₂.

Area of Right Triangles Practice

Calculate the area of right triangles using their two perpendicular legs as base and height (A = ½ × leg₁ × leg₂), distinguishing legs from the hypotenuse.

Area of Shaded Regions & Rings Practice

Solve real-world and mathematical problems involving the area of shaded regions and circular rings (annulus) by subtracting unshaded cutout areas from total outer boundaries.

Area of Shapes Practice

Master calculating the interior area of 2D shapes including rectangles, triangles, parallelograms, trapezoids, and circles using geometric formulas and square units.

Circumference of Circles (Given Diameter) Practice

Master calculating the circumference of circles given diameter d using the direct formula C = πd (with π ≈ 3.14), and distinguishing diameter from radius in visual diagrams.

Circumference of Circles (Given Radius) Practice

Master calculating the circumference of circles given radius r using the formula C = 2πr (with π ≈ 3.14), and interpreting geometric diagrams with radius calipers.

Classifying Angles Practice

Identify and classify angles as acute, right, obtuse, straight, or reflex based on their degree measure.

Classifying Quadrilaterals Practice

Understand that shapes in different categories may share attributes, and classify 4-sided polygons into subcategories based on parallel sides, angle types, and side lengths.

Distance Formula Practice (Coordinate Plane)

Apply the Pythagorean theorem and distance formula d = √((x₂ − x₁)² + (y₂ − y₁)²) to find the distance between two points in a coordinate system.

Exterior Angle Theorem of Triangles Practice

Use informal arguments to establish facts about the exterior angles of triangles, applying the theorem d = ∠A + ∠B.

Finding the Hypotenuse Practice (Pythagorean Theorem)

Apply the Pythagorean theorem a² + b² = c² to determine the unknown length of the hypotenuse in right triangles.

Finding a Missing Leg Practice (Pythagorean Theorem)

Rearrange and solve the Pythagorean theorem a² + b² = c² to calculate an unknown leg length: a = √(c² − b²) or b = √(c² − a²).

Measuring Angles with a Protractor Practice

Measure angles in whole-number degrees using a protractor, selecting the correct scale based on the base ray direction.

Midpoint of a Line Segment Practice

Use the midpoint formula M = ((x₁ + x₂)/2, (y₁ + y₂)/2) to find the point that bisects a line segment into two equal halves.

Parallel Lines Cut by a Transversal Practice

Use informal arguments to establish facts about the angles created when parallel lines are cut by a transversal.

Perimeter by Counting Unit Segments Practice

Master calculating the perimeter of rectangles and rectilinear figures on a unit square grid by counting individual 1-unit line segments along the continuous outer boundary.

Perimeter Finding Missing Sides Practice

Solve for an unknown side length x in triangles, rectangles, squares, and irregular polygons given the total perimeter P and all other side lengths.

Perimeter of Regular Polygons Practice

Calculate the perimeter of regular polygons including pentagons, hexagons, and octagons using the formula P = n × s, and solve for side lengths given total perimeter.

Perimeter of Triangles Practice

Master calculating the perimeter of equilateral, isosceles, and scalene triangles using P = a + b + c, and solving for missing side lengths given total perimeter.

Perimeter of Semicircles Practice

Master calculating the total perimeter of a semicircle by combining the curved half-circumference arc (πr) with the straight diameter base (2r), using P = πr + 2r (with π ≈ 3.14).

Perimeter Practice

Master calculating the perimeter of 2D geometric shapes including rectangles, squares, triangles, and irregular polygons, and solving for missing side lengths given total perimeter.

Pythagorean Triples Practice

Identify, complete, and generate primitive and scaled integer Pythagorean triples satisfying a² + b² = c².

Pythagorean Theorem Practice

Master applying the Pythagorean theorem (a² + b² = c²) to calculate the hypotenuse, find unknown leg lengths, recognize common Pythagorean triples, and solve distance problems in 2D coordinate planes.

Volume of a Sphere Practice

Calculate the volume and surface area of spheres given the radius or diameter using the formulas V = (4/3)πr³ and A = 4πr².

Surface Area of Cones Practice

Calculate the total surface area of a cone by summing its circular base area (πr²) and curved lateral area (πrl) using base radius r and slant height l: SA = πr(r + l).

Surface Area of Cubes Practice

Calculate the total surface area of a cube by multiplying the area of one square face (s²) by 6 congruent faces (SA = 6s²).

Surface Area of Cylinders Practice

Calculate the total surface area of a cylinder by summing the areas of its two circular bases (2πr²) and its unrolled rectangular lateral surface (2πrh): SA = 2πr(r + h).

Surface Area of Square Pyramids Practice

Calculate the total surface area of a square pyramid by summing the area of its square base (s²) and its four congruent triangular lateral faces (4 × ½sl = 2sl): SA = s² + 2sl.

Surface Area of Rectangular Prisms Practice

Calculate the total surface area of a rectangular prism by finding the sum of the areas of its three pairs of opposite rectangular faces: SA = 2(lw + lh + wh).

Surface Area of Spheres Practice

Calculate the total surface area of spheres given the radius or diameter using Archimedes' theorem: SA = 4πr².

Surface Area of Triangular Prisms Practice

Calculate the total surface area of a triangular prism by summing the area of two triangular bases and the three rectangular lateral faces: SA = 2(½ab) + (a + b + c)L = ab + PL.

Vertical & Adjacent Angles Practice

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Volume of Rectangular Prisms with Fractional Edge Lengths Practice

Calculate the volume of right rectangular prisms with fractional and mixed-number edge lengths using the formula V = l × w × h.

Volume of Cones Practice

Calculate the volume of right circular cones using the formula V = ⅓πr²h.

Volume of Cubes Practice

Calculate the volume of cubes given side length using the formula V = s³.

Volume of Cylinders Practice

Calculate the volume of cylinders using the circular cross-section formula V = πr²h.

Volume of Hemispheres Practice

Calculate the volume of hemispheres as exactly half the volume of a sphere: V = ⅔πr³.

Volume of Square Pyramids Practice

Calculate the volume of square pyramids using base area and vertical perpendicular height: V = ⅓s²h.

Volume of Rectangular Prisms Practice

Calculate the volume of rectangular prisms using the formula V = l × w × h = Base Area × height.

Volume of Triangular Prisms Practice

Calculate the volume of triangular prisms by finding base triangle area (½bh) and multiplying by prism length L.

Volume of 3D Geometric Solids

Calculate the volume of prisms, cylinders, pyramids, cones, and spheres using standard formulas.