7. When it is required to prove that two triangles are congruent, how many parts of one must be given equal to corresponding parts of the other? Ans. In general, any three except the three angles. This will be established in Props. viii. and xxvi., taken along with iv.
8. What property of two lines having two common points is quoted in this Proposition? They must coincide.
Exercises.
1. The line that bisects the vertical angle of an isosceles triangle bisects the base perpendicularly.
2. If two adjacent sides of a quadrilateral be equal, and the diagonal bisects the angle between them, their other sides are equal.
3. If two lines be at right angles, and if each bisect the other, then any point in either is equally distant from the extremities of the other.
4. If equilateral triangles be described on the sides of any triangle, the distances between the vertices of the original triangle and the opposite vertices of the equilateral triangles are equal. (This Proposition should be proved after the student has read Prop. xxxii.)
PROP. V.—Theorem.
The angles (ABC, ACB) at the base (BC) of an isosceles triangle are equal to one another, and if the equal sides (AB, AC) be produced, the external angles (DEC, ECB) below the base shall be equal.
