Constructing an isosceles triangle given base and altitude

After doing this	Your work should look like this
We start with two line segments AB and CD that define the altitude and the base length of the triangle.
1.  Draw a point P that will become one end of the base of the triangle.
2.  Place the point of the compasses on the point C and adjust the compasses' width to the desired length CD of the base of the finished triangle
3.  With the compasses' point on P, draw an arc.
4.  Pick a point R anywhere on the arc. This will become the other end of the base of the triangle.
5.  Draw the base line PR.
In the next three steps, we form the perpendicular bisctor of the base
6.  With the compasses' width set roughly to the base length (exact width is not important), draw an arc on each side of the base line from points P and R.
7.  Draw a line through the two arc intersections. This is the perpendicular bisector of the base, dividing it into two equal parts.
8.  Set the compasses' width to the distance from A to B. This is the desired altitude of the triangle.
9.  Place the point of the compasses on the midpoint of the base line, and draw an arc across the perpendicular drawn earlier. This is the third vertex of the triangle.
10.  Draw the two side lines PQ and RQ
11.  Done. The triangle PQR is an isosceles triangle.

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