Monday, January 22, 2024

Geometry+ 02: UNIZOR.COM - Math+ & Problems - Geometry

Notes to a video lecture on http://www.unizor.com

Geometry+ 02

This lecture is dedicated to problems of triangle construction by its certain elements.

The tools of construction are a ruler to draw straight lines and a compass to draw circles.

We will use the following naming rules.
Vertices of triangle will be call by upper case Latin letters A, B and C.
Sides will be called by lower case Latin letters corresponding to opposite vertices: side a is opposite to vertex A etc.
Angles will be called by lower case Greek letters corresponding to names of their vertices: angle α is at vertex A etc.
Medians are named m with a subscript of a side onto which they fall: median ma is from vertex A to side a etc.
Altitudes are named h with similar subscripts, like ha etc.
Angle bisectors are named la etc.
Radius of a circumscribed circle of a triangle is named R.
Radius of an inscribed circle is named r.

Problem A
Construct a triangle by its two sides a, b and a median onto its third side mc.

Problem B
Construct a triangle by its side a and two medians ma and mb.

Hint: Construct ΔBQR where BR=a/2, BQ=2mb/3 and QR=ma/3.

Problem C
Construct a triangle by its three medians ma, mb and mc.

Hint: Construct ΔPQC where CQ=2ma/3, PQ=2mb/3 and CP=2mc/3.

Problem D
Construct a triangle by its side a and two altitudes onto other sides hb and hc.