Geometry Points, Lines, Segments and Angles Worksheet (PDF)

Geometry math worksheet: Points, Lines, Segments and Angles – Maths PDF

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This basics practice worksheet for Geometry covers points, lines, segments and angles (Common Core G-CO.A.1), with a free PDF to print.

These 20 problems practice segment addition, midpoints, angle addition, bisectors and basic definitions (Common Core G-CO.A.1). The first problems are quick one-step checks of the definitions and formulas from the lesson. The middle problems ask for diagrams, equations and careful reasoning in the style of a high school Geometry class. The last six problems are word problems that combine midpoints, angles, clocks and map coordinates.

Geometry · Common Core State Standards: G-CO.A.1

Basics practice worksheet: exercises 1 to 10

Exercise 1 – Length on a number line

Point A is at \(-3\) and point B is at \(9\) on a number line. Find \(AB\).

Exercise 2 – Midpoint on a number line

Find the coordinate of the midpoint of the segment with endpoints at \(4\) and \(18\).

Exercise 3 – Segment addition

Point B lies between A and C.

Find \(AC\).

Exercise 4 – Segment with a variable

Point B is between A and C. \(AB = 3x – 2\), \(BC = x + 8\) and \(AC = 34\). Find \(x\), \(AB\) and \(BC\).

Exercise 5 – Midpoint with a variable

M is the midpoint of segment AB.

Find \(x\) and \(AB\).

Exercise 6 – Angle addition

Ray BD is inside angle ABC.

Find \(m\angle ABC\).

Exercise 7 – Angle bisector

Ray BD bisects \(\angle ABC\) and \(m\angle ABC = 76^{\circ}\). Find \(m\angle ABD\).

Exercise 8 – Bisector with a variable

Ray BD bisects angle ABC.

Ray BD bisects \(\angle ABC\). Find \(x\) and \(m\angle ABC\).

Exercise 9 – Complement and supplement

An angle measures \(37^{\circ}\). Find the measure of its complement and of its supplement.

Exercise 10 – Linear pair

Two angles form a linear pair. Their measures are \((3x + 10)^{\circ}\) and \((5x – 6)^{\circ}\). Find \(x\) and both angle measures.

Exercises 11 and up

Exercise 11 – Midpoint in the plane

Segment AB with its midpoint M.

Find the midpoint of the segment with endpoints \(A(-2, 5)\) and \(B(8, -1)\).

Exercise 12 – Find an endpoint

The midpoint of \(\overline{AB}\) is \(M(1, -2)\) and \(A(-3, 4)\). Find the coordinates of B.

Exercise 13 – Distance in the plane

Find the length of the segment with endpoints \((1, 2)\) and \((7, 10)\).

Exercise 14 – Perpendicular lines

Line \(m\) is perpendicular to line \(n\). One of the four angles they form measures \((2x + 10)^{\circ}\). Find \(x\).

Exercise 15 – Points on a circle

Circle with center O(0, 0).

A circle has center \(O(0, 0)\) and passes through \(P(6, 8)\). Find its radius. Then decide whether \(Q(-10, 0)\) is on the circle.

Exercise 16 – Trail rest stop

Mile markers on a straight trail show a trailhead at mile 3.2 and a lake at mile 11.6. Maya wants a rest stop exactly halfway between them. Find the mile marker of the rest stop and how far it is from each end.

Exercise 17 – Fence line

A straight fence runs from corner post A to corner post C with a gate post B between them. The distance AB is twice the distance BC, and AC is 45 feet. Find AB and BC.

Exercise 18 – Garden path

The path BD bisects the corner angle ABC.

A garden corner forms \(\angle ABC\) with \(m\angle ABC = 120^{\circ}\). A path along ray BD bisects the corner, and \(m\angle ABD = (5x + 10)^{\circ}\). Find \(x\).

Exercise 19 – Angle between clock hands

Clock showing 2:30.

Find the angle between the hour hand and the minute hand at 2:30. Then find the angle at 4:00.

Exercise 20 – Meeting halfway

Each grid square is 1 mile.

On a map grid with 1 mile per square, Ames is at (2, 1) and Bryn is at (10, 7). Liam and Priya, who live in these towns, meet at the midpoint of the straight route between them. Find the meeting point and the distance Liam travels.

Key facts behind this basics practice worksheet

Key facts

Point, line and plane are undefined terms; segments, rays and angles are defined from them.
Segment addition: if B is between A and C, then AB + BC = AC.
A midpoint at coordinate (a + b)/2 splits a segment into two congruent segments.
Angle addition: m∠ABD + m∠DBC = m∠ABC when ray BD is inside the angle.
A circle is all points in a plane at one fixed distance (the radius) from the center.

How to use this basics practice worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the basics practice worksheet as a PDF with the button below and keep it with your notes.

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