Constructing a triangle given two angles and included side (ASA)

After doing this	Your work should look like this
Start with the given line segment and two angles.	Note: The two given angles are only there to indicate the measure of the two angles. The lines making up the given angles have random lengths that have no significance in the construction.
The first part of this construction (steps 1 - 4) is to copy a line segment to form one side of the new triangle. (See Copying a Line Segment).
1.  Mark a point A that will be one vertex of the new triangle.
2.  Set the compasses' width to the length of the segment AB.
3.  With the compasses' point on A, make an arc near the future vertex B of the triangle.
4.  Mark a point B on this arc. Then draw the line AB. This will be one side of the new triangle.
What we do now is essentially copy the two angles. (See Copying an Angle).
5.  With the compasses at any convenient width, draw an arc across both lines of the given angle A.
6.  Without changing the compasses' width, draw an arc at point A on the new triangle. The arc must cross AB and also cross the future side of the 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.  Near point A draw an arc in a similar position so it crosses the arc drawn earlier. This, in effect, 'copies' the measure of the angle at P to the angle at A.
9.  Draw a line from A through the point where the arcs intersect. This will become the second side of the triangle. Draw it long.
10.  Repeat this process at B. Copying the angle measure from the given angle B to the new triangle at B. The point where the lines intersect is C, the third vertex of the triangle.
Done. The blue triangle ABC has the side and two angle measures desired.

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 at a point on a line
• 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
• 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