Elementary plane geometry : inductive and deductive / by Alfred Baker . Angles in a Circle. 89 Since a quadrilateral can be divided into two tri-angles by joining its opposite angles, the snm of allthe angles of any quadrilateral is four right anglesiHence if the sum of a pair of opposite angles be tworight angles, the sum of the other pair is two rightangles 4. Describe a circle, and inthe semicircle construct a num-ber of angles as indicated in thefigure. Adjust the protractor tothe angles ADB, AEB, ....What is the magnitude of theseangles ? The magnitude of the anglein a semicircle m
Elementary plane geometry : inductive and deductive / by Alfred Baker . Angles in a Circle. 89 Since a quadrilateral can be divided into two tri-angles by joining its opposite angles, the snm of allthe angles of any quadrilateral is four right anglesiHence if the sum of a pair of opposite angles be tworight angles, the sum of the other pair is two rightangles 4. Describe a circle, and inthe semicircle construct a num-ber of angles as indicated in thefigure. Adjust the protractor tothe angles ADB, AEB, ....What is the magnitude of theseangles ? The magnitude of the anglein a semicircle may be j^roved thus : The straightangle ACB at the centre is (Ch. XII., 1) double any ofthe angles at the circumference. But the straight angleACB is 180°. Hence the angle in a semicircle is90°. ADB being a right-angledtriangle, find the centre ofthe circle through A, D andB, by bisecting AD, BD anddrawing the perpendicularsEC, FC. Note that these perpendiculars intersect in AB; and note also that C,being the centre of the circle through A, D and B, thecentre of the hypotenuse of a right-angled triangle isequidistant from the three angles of the triangle.
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