...71), is greater than C. Hence Z ABC is greater than Z C. PROPOSITION XXVIII. THEOREM. 95. CONVERSELY, if two angles of a triangle are unequal, the sides opposite are unequal, and the greater side lies opposite the greater angle. A In the triangle ABC let the angle ABC ber greater than the angle...

...BD, CD, show that DBCvri\\ be an isosceles triangle. PROPOSITION XXXII. THEOREM. 159. CONVERSELY : If two angles of a triangle are unequal, the sides opposite are unequal, and tlie greater side is opposite the greater angle. In the triangle ACB, let angle ACB be greater than...

...a circle whose radius is 4 feet. (Obtain result correct to two places of decimals.) 3 4 Prove that if two angles of a triangle are unequal, the sides...and the greater side is opposite the greater angle. 5 5 Prove that an angle formed by a tangent and a secant intersecting without a circle is measured...

...contradicts the hypothesis that angle b — angle c. Hence AC=AB. QE D / PROPOSITION XXI. THEOREM VS. If two angles of a triangle are unequal, the sides...greater side is opposite the greater angle. [Converse of Proposition XIX.] GIVEN in the triangle ABC, the angle a > angle c. To PROVE side ^C>side AB. AB is...

...unequal, the angles opposite are unequal, and the greater angle is opposite the greater side. 159. If two angles of a triangle are unequal, the sides...and the greater side is opposite the greater angle. 160. Two triangles are equal if the three sides of the one are equal respectively to the three sides...

...AC=AB. QE D PROPOSITION XXI. THEOREM 78. If two angles of a triangle are unequal, the opposite sides are unequal, and the greater side is opposite the greater angle. [Converse of Proposition XIX.] GIVEN in the triangle ABC, the angle a > angle c, To PROVE side 5C>side AB. Either...

...AC=AB. QE D PROPOSITION XXI. THEOREM 78. If two angles of a triangle are unequal, the opposite sides are unequal, and the greater side is opposite the greater angle. [Converse of Proposition XIX.] GIVEN in the triangle ABC, the angle a >angle c. To PROVE side £C> side AB. Either...

...ABD^is > ZC, Then, since Z ABC is > Z ABD, and v PROP. XXXIII. THEOREM. 99. (Converse of Prop. XXXII.) If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side lies opposite the greater angle. J> Given, in A ABC, Z ABC >ZC To Prove AC>AB. Proof. Draw line BD,...

...angle ? 2. Which side of a right triangle is the greatest? Theorem. The greater side of a triangle lies opposite the greater angle. (Converse of Prop. XXVIII)...that Z ABD — Z BAD. Then, § 118, AD = BD. In A BOD, § 125, BD + DOBC. Substituting AD for its equal BD, AD + DOBC, or AC>BC. That is, AC, opposite...

...angle ? 2. Which side of a right triangle is the greatest? Theorem. The greater side of a triangle lies opposite the greater angle. (Converse of Prop. XXVIII)...BC, opposite angle A. Proof. Draw BD so that Z ABD = </ BAD. Then, § 118, AD = BD. In ABCD, § 125, BD + DOBC. Substituting AD for its equal BD, AD +...