Geometry Constructor

Geometry you can move. Drag the points of a triangle or circle and watch the angles and lengths change while the theorem stays true. Follow compass-and-ruler constructions one step at a time, or build and measure your own.

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Theorems you can explore

Theorem	Statement
Angle sum of a triangle	The three angles add up to 180°.
Exterior angle	An exterior angle equals the sum of the two opposite interior angles.
Isosceles triangle	Angles opposite equal sides are equal.
Pythagoras	In a right-angled triangle, c² = a² + b².
Semicircle	The angle in a semicircle is 90°.
Angle at the centre	The angle at the centre is twice the angle at the circumference on the same arc.
Same segment	Angles in the same segment of a circle are equal.
Tangent	A tangent is perpendicular to the radius at the point of contact.
Midpoint theorem	The line joining two midpoints is parallel to the third side and half as long.
Cyclic quadrilateral	Opposite angles add up to 180°.
Triangle centres	Medians, perpendicular bisectors, angle bisectors and altitudes each meet at one point.

Tips for constructing

In Construct, choose a tool and click on the picture. Click an empty place to make a new point, or click on an existing point to reuse it.
Clicking exactly where two lines or circles cross marks their intersection. These points stay attached, so they move when you drag the points the lines were built from.
A compass circle is made by clicking the centre and then a point on the circle: the distance between them is the compass opening.
Use Distance and Angle to check your work, then drag the blue points to test it in other positions. A real construction works for every position.

Practise what you learned

Test yourself with chapter-wise MCQs and explanations:

Trigonometric Identities of Sum and Difference of Angles — Maths, HSSC-KPK First Year (1,157 questions)
Plane Analytic Geometry - Straight Line — Maths, HSSC-KPK Second Year (1,497 questions)
Introduction to Coordinate Geometry — Maths, SSC-KPK Class 9 (241 questions)
Congruent Triangles — Maths, SSC-KPK Class 9 (202 questions)
Parallelograms and Triangles — Maths, SSC-KPK Class 9 (196 questions)
Line Bisectors and Angle Bisectors — Maths, SSC-KPK Class 9 (126 questions)
Sides and Angles of a Triangle — Maths, SSC-KPK Class 9 (132 questions)
Practical Geometry - Triangles — Maths, SSC-KPK Class 9 (696 questions)
Projection of a Side of a Triangle — Maths, SSC-KPK Class 10 (549 questions)
Chords of a Circle — Maths, SSC-KPK Class 10 (588 questions)
Tangent to a Circle — Maths, SSC-KPK Class 10 (594 questions)
Angle in a Segment of a Circle — Maths, SSC-KPK Class 10 (523 questions)
Practical Geometry — Maths, SSC-KPK Class 10 (748 questions)
Coordinate Geometry — Maths, SSC-Punjab Class 9 (1,055 questions)
Chords and Arcs of a Circle — Maths, SSC-Punjab Class 10 (584 questions)
Tangent and Angles of a Circle — Maths, SSC-Punjab Class 10 (816 questions)
Practical Geometry of Circles — Maths, SSC-Punjab Class 10 (540 questions)

On screen 40 pixels equal 1 cm, so lengths are shown in centimetres on a fixed scale. Your own construction is saved in this browser. Works offline: after your first visit the tool is saved in your browser.