Plane and solid geometry . ting line AC, and by steps similar to 1-8. 10. Same reason as 4. 11. Substituting for its equal A ACG. 12. By proof. 154. Cor. From a point outside a linethere ejoists only one perpendicular tothe line. Hint. If there exists a second JL to AB fromP, as FC, then Z. PC A and Z P^^ are both rt. A B C K and are therefore equal. But this is impossible by § 153- 155. §§ 149 and 154 may be combined in one statement asfollows: From a point outside a line there exists one and only one per*pendicular to the line. Ex. 148. A triangle cannot contain two right angles. Ex. 1
Plane and solid geometry . ting line AC, and by steps similar to 1-8. 10. Same reason as 4. 11. Substituting for its equal A ACG. 12. By proof. 154. Cor. From a point outside a linethere ejoists only one perpendicular tothe line. Hint. If there exists a second JL to AB fromP, as FC, then Z. PC A and Z P^^ are both rt. A B C K and are therefore equal. But this is impossible by § 153- 155. §§ 149 and 154 may be combined in one statement asfollows: From a point outside a line there exists one and only one per*pendicular to the line. Ex. 148. A triangle cannot contain two right angles. Ex. 149. In the figure of Prop. XIV, is angle DCB necessarily greateithan angle BCA ? than angle B ? Ex. 150. In Fig. 1, prove that: (1) Angle 1 is greater than angle CAE or angle AEC; (2) Angle 5 is greater than angle CBA or angle BAE; (3) Angle EDA is greater than angle 3 ; (4) Angle 4 is greater than angle DAE. Ex. 151. In Fig. 2, show that angle 6 isgreater than angle 7 ; also that angle 9 isgreater than angle A, Fia. 54 PLANE GEOMETRY Proposition XV. Theorem 156. If two sides of a triangle are unequal, the angleopposite the greater side is greater than the angle oppositethe less side.
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