Book I, Proposition 8

Problems

1.  a)  State the hypothesis of Proposition 8.

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Two triangles have two sides equal to two sides respectively, and the bases are also equal.

1.  b)  State the conclusion.

The angles are equal that are contained by the equal sides.

2.  The vertices of triangle ABC are on the circumference of a circle with
2.  center D, and angle ABC is equal to angle ACB.  Prove that angle
2.  ADB is equal to angle ADC.

Since ABC is a circle with center D, the straight line DB
is equal to the straight line DC; (Def. 15)
and AD is a common side of triangles ADB, ADC;
therefore the two sides AD, DB are equal to the two sides AD, DC respectively.
And the base AB is equal to the base AC,
because angle ABC is equal to angle ACB. (I, 6.)
Therefore those angles are equal that are contained by the equal sides of triangles ADB, ADC:  (S.S.S.)
angle ADB is equal to angle ADC.

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