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Quizzes > High School Quizzes > Mathematics

LEAP 2025 Geometry Practice Test

Boost your test readiness with clear geometry skills

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art promoting The Leap 2025 Geometry Challenge quiz for high school students

What is the sum of the interior angles of a triangle?
360°
180°
90°
270°
The interior angles of any triangle always add up to 180°. This is a fundamental property in Euclidean geometry.
What is the formula for the area of a circle?
πr
2πr
2πr²
πr²
The area of a circle is given by the formula πr², where r is the radius. This formula is one of the basic building blocks in geometry.
What is a right angle?
90°
180°
45°
360°
A right angle measures exactly 90°. Recognizing right angles is essential for understanding many geometric figures.
Which shape has all sides equal and all angles equal?
Trapezoid
Square
Rectangle
Rhombus
A square has all sides of equal length and each interior angle is 90°. This complete symmetry makes it uniquely regular among quadrilaterals.
What is an isosceles triangle?
A triangle with one 90-degree angle
A triangle with no equal sides
A triangle with at least two equal sides
A triangle with all sides equal
An isosceles triangle is defined by having at least two sides of equal length. This property also implies that the base angles opposite those sides are equal.
What is the sum of the interior angles in a quadrilateral?
360°
540°
180°
720°
The interior angles of any quadrilateral sum to 360°. This well-known property applies to all simple (non-self-intersecting) quadrilaterals.
Which theorem relates the lengths of the sides in a right triangle?
Pythagorean theorem
Law of Sines
Euclid's theorem
Triangle Sum theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It is one of the most vital concepts in geometry.
If two angles are complementary, what is their sum?
90°
60°
120°
180°
Complementary angles are defined as two angles whose measures add up to 90°. This concept frequently appears in problems involving right triangles.
What is the area of a parallelogram with a base of 8 units and a height of 5 units?
20
80
13
40
The area of a parallelogram is calculated as the product of its base and height. Multiplying 8 by 5 gives an area of 40 square units.
An inscribed angle that intercepts a semicircle in a circle measures:
45°
180°
60°
90°
By Thales' theorem, an inscribed angle that intercepts a semicircle is always a right angle, measuring 90°. This is a classical result in circle geometry.
Which statement is true about the diagonals of a rectangle?
They are not equal in length
They bisect each other at right angles
They are parallel
They are congruent
In a rectangle, the diagonals are equal in length and bisect each other. However, they are not necessarily perpendicular unless the rectangle is a square.
What is the measure of each exterior angle of a regular hexagon?
45°
60°
120°
90°
The sum of the exterior angles for any polygon is always 360°. Dividing 360° by 6 (for a hexagon) results in an exterior angle of 60°.
If two triangles are similar and the sides of one triangle are 3, 4, 5 while the shortest side of the similar triangle is 6, what is the length of its longest side?
15
10
12
9
The ratio of similarity is found by dividing the corresponding sides; 6 divided by 3 gives a factor of 2. Multiplying the longest side (5) by 2 results in 10.
What is the volume of a prism with a base area of 12 square units and a height of 7 units?
64
78
84
19
The volume of a prism is determined by multiplying the area of the base by its height. Here, 12 multiplied by 7 yields a volume of 84 cubic units.
A circle has a diameter of 10 units. What is its radius?
5
2.5
10
20
The radius of a circle is half of its diameter. Thus, a diameter of 10 units results in a radius of 5 units.
According to the Alternate Segment Theorem, if the angle between a tangent and chord of a circle is 35°, what is the measure of the inscribed angle in the alternate segment?
35°
145°
70°
140°
The Alternate Segment Theorem tells us that the angle between a tangent and a chord is equal to the angle in the opposite (alternate) segment. Therefore, if the tangent-chord angle is 35°, the corresponding inscribed angle is also 35°.
Find the distance between the points (3, -2) and (-1, 4) in the coordinate plane.
2√7
2√13
8
2√10
The distance formula is used here: √[(3 - (-1))² + (-2 - 4)²] becomes √(4² + (-6)²), which simplifies to √(16 + 36) = √52, or 2√13. This calculation confirms the distance.
A triangle has side lengths 7, 24, and 25. What type of triangle is it?
Equilateral Triangle
Obtuse Triangle
Right Triangle
Acute Triangle
By applying the Pythagorean theorem, we find that 7² + 24² equals 25² (49 + 576 = 625). This confirms that the triangle is a right triangle.
In a circle with radius 5 units, chord AB is 8 units long. What is the distance from the center of the circle to chord AB?
4
3
2
5
The perpendicular distance from the center to a chord can be determined using the Pythagorean theorem. With half the chord length being 4 and the radius 5, the distance is √(5² - 4²) = √(25 - 16) = √9 = 3 units.
Which formula correctly represents the area of a regular pentagon in terms of its side length (s) and apothem (a)?
½ × perimeter × apothem
½ × side × apothem
perimeter × apothem
side × apothem
The area of any regular polygon is given by ½ × (perimeter) × (apothem). For a regular pentagon, the perimeter is 5s, so the formula becomes ½ × 5s × a.
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Study Outcomes

  1. Analyze fundamental geometric figures and their properties.
  2. Apply geometric theorems to solve problems.
  3. Evaluate relationships between angles and parallel lines.
  4. Synthesize problem-solving strategies for complex geometric challenges.
  5. Assess and reflect on understanding of key geometric concepts.

LEAP 2025 Geometry Practice Test Cheat Sheet

  1. Master the Pythagorean Theorem - In any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It's like geometric magic for determining lengths without ever measuring! Once you see how those squares fit together, you'll feel unstoppable tackling triangle problems. Geometry Formulas and Other Important Stuff You Should Know
  2. Understand Triangle Congruence Criteria - Use SSS, SAS, ASA, and AAS to check if two triangles are exactly the same size and shape. It's like matching puzzle pieces: three sides or angles in the right combo guarantee a perfect fit. Mastering these shortcuts means fewer headaches on proof-based questions! Geometry Study Guides
  3. Learn Special Right Triangle Properties - In a 45°-45°-90° triangle, the legs are twins and the hypotenuse is √2 times a leg; in a 30°-60°-90°, the hypotenuse is twice the short leg and the long leg is √3 times the short one. Think of them as the VIP triangles that save you time instead of using Pythagoras every time. Knowing these ratios by heart lets you breeze through many exam questions. Geometry Formulas and Other Important Stuff You Should Know
  4. Familiarize Yourself with Circle Formulas - The circumference (perimeter of a circle) is 2πr and the area is πr². These aren't just fancy Greek symbols - they're your ticket to cracking any circle problem, from arc lengths to sector areas. Practice a few examples and you'll see how quickly these pop back into memory. Geometry Formulas and Other Important Stuff You Should Know
  5. Practice Distance & Midpoint Formulas - To find the distance between (x₝, y₝) and (x₂, y₂), use √[(x₂ - x₝)² + (y₂ - y₝)²]; the midpoint is ((x₝ + x₂)/2, (y₝ + y₂)/2). It's like measuring with a digital ruler and then pinpointing the exact halfway spot. Solid practice ensures you'll never mix them up under exam pressure! Geometry Formulas and Other Important Stuff You Should Know
  6. Understand Parallelogram Properties - Opposite sides are equal and parallel, opposite angles match, and the diagonals bisect each other into equal halves. Picture a leaning box - those symmetry rules keep everything in check. These traits make area and coordinate problems a cinch once you internalize them. Geometry Study Guides
  7. Learn Transformations - Translations shift figures, rotations spin them, reflections flip them, and dilations resize them. It's like playing with shapes in a digital art program - each move follows strict rules and helps you predict new positions. Mastering these operations ties neatly into coordinate geometry and visual proofs! Geometry Study Guides
  8. Study Similar Triangles - When triangles are similar, corresponding angles match and sides are proportional. This is the secret sauce for solving real-world scaling problems, like map distances or architectural models. Spotting triangles "in disguise" will save you tons of calculation time! Geometry Study Guides
  9. Understand Trigonometry Basics - Sine, Cosine, and Tangent relate angles to side lengths in right triangles - SOH-CAH-TOA is your trusty mnemonic. These ratios unlock problems involving heights, angles of elevation, and oscillations. Practicing a handful of triangle puzzles will cement these definitions forever! High School Geometry
  10. Know the Equation of a Circle - The form (x - h)² + (y - k)² = r² tells you a circle's center (h, k) and radius r. It's like coding a perfect circle in the coordinate plane. Mastering this lets you solve locus problems and intersection puzzles with confidence! Geometry Formulas and Other Important Stuff You Should Know
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