Exercises.
1. Trisect a right angle.
2. Any angle of a triangle is obtuse, right, or acute, according as the opposite side is greater than, equal to, or less than, twice the median drawn from that angle.
3. If the sides of a polygon of n sides be produced, the sum of the angles between each alternate pair is equal to 2(n − 4) right angles.
4. If the line which bisects the external vertical angle be parallel to the base, the triangle is isosceles.
5. If two right-angled △s ABC, ABD be on the same hypotenuse AB, and the vertices C and D be joined, the pair of angles subtended by any side of the quadrilateral thus formed are equal.
6. The three perpendiculars of a triangle are concurrent.
7. The bisectors of two adjacent angles of a parallelogram are at right angles.
8. The bisectors of the external angles of a quadrilateral form a circumscribed quadrilateral, the sum of whose opposite angles is equal to two right angles.
9. If the three sides of one triangle be respectively perpendicular to those of another triangle, the triangles are equiangular.