Constructing a triangle given two sides and included angle (SAS)

After doing this	Your work should look like this
Start with two line segments and the included angle.
1.  Mark a point A that will be one vertex of the new triangle.
2.  Draw a ray from point A. This will become the side AB of the new triangle, so make it longer than AB.
3.  Set the compasses' width to the length of the given side AB.
4.  Set the compasses on A, and mark a point B on the ray just drawn.
5.  With the compasses set to any convenient width, from the point A on the given angle, draw an arc across both lines..
6.  Without changing the compasses' width, draw a similar sized arc at point A on the new triangle.
7.  Set the compasses to the arc width at the given angle A. This the distance between the points where the arc intersects the sides of the angle.
8.  Make a similar arc on the new triangle so it crosses the previous arc.
9.  Draw a ray from A, through where the arcs intersect and onwards. This will become side AC of the triangle so make it longer than AC.
10.  Set the compasses' width to the distance AC.
11.  With the compasses on A, make an arc across the second ray, creating point C.
12.  Draw the line BC, the third side of the triangle
Done, the triangle ABC has the desired two side lengths and included angle.

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Other constructions pages on this site

• List of printable constructions worksheets

Lines

• Introduction to constructions
• Copy a line segment
• Sum of n line segments
• Difference of two line segments
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts
• Parallel line through a point (angle copy)
• Parallel line through a point (rhombus)
• Parallel line through a point (translation)

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Sum of n angles
• Difference of two angles
• Supplementary angle
• Complementary angle
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Isosceles triangle, given leg and apex angle
• Equilateral triangle
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two angles and non-included side (aas)
• Triangle, given two sides and included angle (sas)
• Triangle medians
• Triangle midsegment
• Triangle altitude
• Triangle altitude (outside case)

Right triangles

• Right Triangle, given one leg and hypotenuse (HL)
• Right Triangle, given both legs (LL)
• Right Triangle, given hypotenuse and one angle (HA)
• Right Triangle, given one leg and one angle (LA)

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Tangents to two circles (external)
• Tangents to two circles (internal)
• Incircle of a triangle
• Focus points of a given ellipse
• Circumcircle of a triangle

Polygons

• Square given one side
• Square inscribed in a circle
• Hexagon given one side
• Equilateral triangle inscribed in a given circle
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object