Book I. Propositions 31 and 32 Back to Propositions 31, 32. 11.
Solve the problem of Proposition 31: Through a given point to
draw straight line parallel to a given straight line. To see the
answer, pass your mouse over the colored area. Let A be the
given point, and BC the given straight line; Choose any point D
on BC, and draw AD; the straight line AD, which meets the two
straight lines EF, BC makes the alternate angles EAD, ADC equal.
Therefore EF is parallel to BC. (I. 27) 12. a) State the
hypothesis of Proposition 32. A figure is a triangle and one
side is extended. 2. b) State the conclusion. The exterior angle
is equal to the two opposite interior angles; and the three
interior angles of a triangle are equal to two right angles. 2.
c) Practice Proposition 32. 13. Prove Proposition 32 by drawing
a straight line DE through A 3. This proof is attributed to
Pythagoras, who lived some 250 years Because DE is parallel to
BC, 14. ABC is a circle with center D; ABD is a triangle; and
ADC is a 14. straight line