Geometry Fundamentals I Practice Questions with Answers and a Guided Lesson
Use the question set below to practice geometry fundamentals: points, lines, line segments, and rays, angles (acute, right, obtuse, straight), triangle facts (angle sum, types of triangles, Pythagorean theorem), quadrilaterals (rectangle, square, parallelogram, rhombus, kite, trapezoid), circles (radius, diameter, circumference, area), perimeter and area, symmetry, and polygon angle sums. If you want a refresher, click Start lesson to open a step-by-step guide with examples and quick checks.
Answer the question set and review your mistakes at the end.
How this geometry practice works
1. Take the practice set: answer the geometry questions below.
2. Open the lesson (optional): review key geometry definitions, formulas, and angle facts with worked examples.
3. Retry: return to the question set and apply the geometry rules immediately.
What you will learn in the Geometry Fundamentals I lesson
Points, lines, and angles
Point, line, segment, ray (the building blocks of geometry)
Purpose: Build a strong foundation in geometry fundamentals—the core ideas you need for angles, triangles, quadrilaterals, circles, perimeter, area, symmetry, and polygon angle sums.
Success criteria
Use basic geometry language: point, line, line segment, ray, and plane.
Recognize parallel, perpendicular, and intersecting lines.
Classify angles: acute, right, obtuse, straight and use relationships like complementary (\(90^\circ\)) and supplementary (\(180^\circ\)).
Use triangle facts: angle sum \(180^\circ\), triangle types, and the Pythagorean theorem \(a^2+b^2=c^2\) (right triangles only).
Identify common quadrilaterals and their properties: rectangle, square, parallelogram, rhombus, kite, trapezoid.
Use circle vocabulary and formulas: radius, diameter, circumference \(C=2\pi r=\pi d\), and area \(A=\pi r^2\).
Compute perimeter and area of rectangles, squares, and triangles with correct units.
Use polygon angle facts: exterior angles sum to \(360^\circ\) (any convex polygon) and interior angle sum is \((n-2)180^\circ\).
Key vocabulary
Point: an exact location (no length or width).
Line: goes on forever in both directions.
Line segment: part of a line with two endpoints.
Ray: starts at one endpoint and goes forever in one direction.
Angle: formed by two rays with a common endpoint (vertex).
Parallel lines: lines in a plane that never meet.
Perpendicular lines: intersect to form a right angle (\(90^\circ\)).
Polygon: a closed figure made of straight line segments.
Radius / diameter: \(d=2r\) in a circle.
Perimeter / area: distance around vs. space inside a shape.
Line of symmetry: a line that folds a shape into matching halves.
Quick pre-check
Pre-check 1: How many degrees are in a straight angle?
Hint: A straight angle looks like a straight line (half of a full turn).
Pre-check 2: How many vertices (corners) does a triangle have?
Hint: A triangle has 3 sides, so it also has 3 corners.
Lines & Angles
Lines, rays, and angle relationships
Learning goal: Recognize basic geometric objects and use key angle facts to solve quick geometry questions.
Key ideas
Parallel lines never meet, and perpendicular lines meet at a right angle (\(90^\circ\)).
An angle is measured in degrees: a full turn is \(360^\circ\), a straight angle is \(180^\circ\), and a right angle is \(90^\circ\).
Complementary angles add to \(90^\circ\). Supplementary angles add to \(180^\circ\).
When two lines intersect, vertical angles are equal.
Worked example
Example: Two angles are supplementary. One angle is \(70^\circ\). Find the other angle.
Supplementary means the sum is \(180^\circ\). \[\text{Other angle}=180^\circ-70^\circ=110^\circ.\]
Try it
Try it 1: Two lines intersect. One angle measures \(120^\circ\). What is the measure of its vertical angle?
Hint: Vertical angles are always equal.
Try it 2: What is the measure of each interior angle in a square?
Hint: A square has four right angles, and a right angle is \(90^\circ\).
Summary
Complementary: sum \(90^\circ\). Supplementary: sum \(180^\circ\).
Vertical angles are equal when lines intersect.
Squares have right angles, so each interior angle is \(90^\circ\).
Triangles
Triangle facts and right triangles
Learning goal: Use triangle angle sums, triangle types, and the Pythagorean theorem for right-triangle problems.
Key ideas
Triangle angle sum: the three interior angles always add to \(180^\circ\).
Right triangle: has one \(90^\circ\) angle. The side opposite the right angle is the hypotenuse (the longest side).
Pythagorean theorem (right triangles only): if the legs are \(a\) and \(b\) and the hypotenuse is \(c\), then \(a^2+b^2=c^2\).
Isosceles triangle: has two equal sides and one line of symmetry.
Worked example
Example: A triangle has angles \(50^\circ\) and \(60^\circ\). What is the third angle?
Use the angle sum \(180^\circ\): \[\text{Third angle}=180^\circ-(50^\circ+60^\circ)=180^\circ-110^\circ=70^\circ.\]
Try it
Try it 1: What is the length of the hypotenuse in a right triangle with legs \(6\) and \(8\)?
Area & perimeter: square \(A=s^2\), triangle \(A=\dfrac{1}{2}bh\), rectangle \(P=2(l+w)\).
Polygons: interior sum \((n-2)180^\circ\); exterior sum \(360^\circ\) (convex).
Next step: Close this lesson and try your quiz again. If you miss a question, reopen the book and review the page that matches the geometry skill you need.
