Get ready to conquer ACT Prep Geometry Questions with our free scored quiz! Whether you're hunting for extra act prep geometry practice or tackling tough ACT geometry problems, this geometry quiz online will test area formulas, triangle theorems, circle proofs, and even geometric sequences practice to strengthen your reasoning. From mastering circle theorems to solving tricky proofs under time pressure, you'll gain confidence and sharpen your problem-solving speed. If you've enjoyed our geometry chapter 1 test or breezed through some area of a triangle practice problems, this challenge ramps up the stakes. Jump in now - see your instant results and track your progress today!
What is the area of a triangle with a base of 10 units and a height of 5 units?
15
25
100
50
The area of a triangle is 1/2 × base × height, so 1/2 × 10 × 5 = 25 square units. This formula applies to all triangles regardless of orientation. Practicing basic area calculations is essential for ACT geometry. Learn more: triangle area.
What is the sum of the interior angles of a convex hexagon?
900°
720°
360°
540°
The sum of interior angles of an n-sided polygon is (n-2) × 180°, so for a hexagon (6 sides): (6-2)×180° = 720°. This formula is key for solving polygon angle problems on the ACT. More details: polygon angles.
A square has a side length of 6 units. What is its perimeter?
36
18
12
24
A square's perimeter is 4 times its side length: 4 × 6 = 24 units. Recognizing shape-specific formulas quickly can save time on the ACT. See: square perimeter.
What is the circumference of a circle with a radius of 3 units? (Use ? for pi.)
9?
3?
6?
18?
Circumference is 2?r, so with r = 3: 2 × ? × 3 = 6?. Familiarity with basic circle formulas is crucial for ACT geometry questions. Reference: circle formulas.
What is the area of a circle with a radius of 4 units? (Use ? for pi.)
16?
8?
32?
12?
Circle area is ?r², so ? × 4² = 16? square units. Questions involving circle area are common on the ACT, so mastering this formula is important. More information: area of a circle.
In a right triangle, the legs measure 6 and 8 units. What is the length of the hypotenuse?
14
12
8
10
By the Pythagorean theorem, c = ?(6²+8²) = ?(36+64) = ?100 = 10 units. Pythagorean triples like (6,8,10) frequently appear on standardized tests. See: Pythagorean theorem.
What is the slope of the line passing through the points (2, 3) and (5, 11)?
3/8
2/3
4/5
8/3
Slope is (y? - y?)/(x? - x?) = (11 - 3)/(5 - 2) = 8/3. Understanding slope calculations is vital for ACT coordinate geometry problems. Learn more: two-point form.
In a right triangle, an altitude is drawn to the hypotenuse, dividing it into segments of lengths 4 and 9. What is the length of this altitude?
6
12
5
3
The altitude to the hypotenuse in a right triangle equals ?(segment1×segment2) = ?(4×9) = 6. This geometric mean property often appears on advanced ACT questions. See: right triangle altitude.
Two chords intersect inside a circle, creating arcs measuring 80° and 100°. What is the measure of the angle between those chords?
45°
90°
80°
100°
An angle formed by intersecting chords equals half the sum of the intercepted arcs: (80°+100°)/2 = 90°. Problems involving chord theorems are common on the ACT. More: intersecting chords.
What is the area of a trapezoid with bases of lengths 10 and 6 units and a height of 4 units?
24
16
32
40
Trapezoid area = (base1 + base2)/2 × height = (10+6)/2 × 4 = 32. ACT questions often test the ability to apply area formulas accurately. Reference: trapezoid area.
Triangle ABC has sides of lengths 6, 8, and 10 units. What is its area?
24
20
18
48
Use Heron's formula: s = (6+8+10)/2 = 12, so area = ?(12×6×4×2) = ?576 = 24. Heron's formula problems occasionally appear on ACT geometry sections. More details: Heron's formula.
What are the coordinates of the midpoint of the segment connecting (?2, 7) and (4, ?1)?
(1, ?3)
(2, 3)
(2, ?1)
(1, 3)
Midpoint is ((?2+4)/2, (7+ (?1))/2) = (1,3). This formula is fundamental for coordinate geometry questions on standardized tests. Reference: coordinate geometry.
Two secants intersect outside a circle, intercepting arcs of 100° and 40°. What is the measure of the angle formed between the secants?
60°
70°
50°
30°
An angle formed by two secants outside the circle equals half the difference of the intercepted arcs: (100°?40°)/2 = 30°. This theorem is tested in challenging ACT geometry questions. Learn more: secant-secant angle.
A point outside a circle is 10 units from the center, and the circle's radius is 6 units. What is the length of the tangent from the point to the circle?
6
10
8
12
The tangent length from an external point is ?(d²?r²) = ?(10²?6²) = ?(100?36) = 8. Mastering tangent-secant theorems is valuable for expert-level geometry. See: tangent-secant theorem.
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Study Outcomes
Solve Area and Perimeter Problems -
Use ACT prep geometry questions to calculate the area and perimeter of circles, triangles, and polygons with confidence.
Apply Theorems and Properties -
Apply key geometric theorems - such as the Pythagorean theorem and properties of parallel lines - to tackle ACT geometry problems accurately.
Analyze Geometric Sequences -
Recognize and solve geometric sequences practice questions by determining common ratios and term relationships.
Identify Shape Characteristics -
Determine and use properties of angles, sides, and symmetry to solve a variety of ACT geometry problems.
Interpret and Deconstruct Diagrams -
Break down complex geometry quiz online figures to extract essential information and answer questions efficiently.
Cheat Sheet
Pythagorean Theorem & Triangle Classifications -
Master a² + b² = c² for all right triangles, a staple in act prep geometry questions and ACT geometry problems. Remember the 3-4-5 and 5-12-13 triples as mnemonics for quick integer checks - 3-4-5 is your "go-to" example in many geometry quiz online platforms (Khan Academy).
Area Formulas for Common Polygons -
Recall A = ½bh for triangles, A = bh for parallelograms, and A = (b + b₂)/2 × h for trapezoids - these formulas appear repeatedly in act prep geometry practice guides. Sketching each shape and labeling dimensions can boost accuracy and speed under timed conditions (College Board official materials).
Circle Properties & Theorems -
Use A = πr² and C = 2πr for area and circumference, and remember that inscribed angles subtended by the same arc are equal - vital for angle-chasing problems. The "pie-rate" pun (π·r) helps you recall both formulas, a trick endorsed by MIT OpenCourseWare.
Geometric Sequences & Series -
Identify terms using aₙ = a·r❿❻¹ and sum series with Sₙ = a(1 − r❿)/(1 − r) when reviewing geometric sequences practice questions. This pattern shows up in problems about area growth or fractal designs, as explained in depth by Cornell University's math tutorials.
Coordinate Geometry Essentials -
Memorize the distance formula d = √[(x₂ − x)² + (y₂ − y)²], slope m = (y₂ − y)/(x₂ − x), and midpoint ((x + x₂)/2, (y + y₂)/2) for ACT geometry problems. Plotting points and drawing figures on graph paper during real act prep geometry questions can help visualize solutions quickly (American Mathematical Society).
