...the theorem follows by § 40.) 76. Cor. n. //' two parallels are cut by a transversal, the sum of the interior angles on the same side of the transversal is equal to two right angles. (Fig. of Prop. XXI.) Given Us AB and CD cut by transversal EF at points G and H, respectively. To Prove...

...the theorem follows by § 40.) 76. Cor. II. If two parallels are cut by a transversal, the sum of the interior angles on the same side of the transversal is equal to two riyht angles. (Fig. of Prop. XXI.) Given IIs AB and CD cut by transversal EF at points G and H, respectively....

...Prove that the alternate-exterior angles are equal, or Z EGA = Z DHF, or Z EGB = Z ClIF. 2. Prove that the sum of the two interior angles on the same side of the cutting line, or transversal, are equal to two right angles. SUGGESTION. /.AGH= Z GHD ; add Z GHC....

...non-parallel sides of a trapezoid and the other is equal to half the sum of the parallel sides. § 160 2. Two lines are parallel, a. If both are perpendicular...side of the transversal is equal to two right angles. § 79 e. If both are parallel to a third line. § 80 /. If they are the bases of a trapezoid. § 138...

...the same line. § 71 6. If when cut by a transversal the alternate interior angles are equal. § 76 c. If when cut by a transversal the corresponding...side of the transversal is equal to two right angles. § 79 e. If both are parallel to a third line. § 80 /. If they are the bases of a trapezoid. § 138...

...79. Cor. II. (Converse of § 76.) If two straight lines are cut by a transversal, and the sum of the interior angles on the same side of the transversal is equal to two right angles, the two lines are parallel. (Fig. of Prop. XXII.) Given lines AB and CD cut by transversal EF at points...

...79. Cor. II. (Converse of § 76.) If two straight lines are cut by a transversal, and the sum of the interior angles on the same side of the transversal is equal to two right angles, the two lines are parallel. (Fig. of Prop. XXII.) Given lines AB and CD cut by transversal EF at points...

...Z, and a = 2 d, how large is each of the other angles ? 65. If a transversal cuts two lines making the sum of the two interior angles on the same side of the transversal a straight angle, one of them being 30° 27', how large is each of the other angles ? PROPOSITION XVIII....

...- 35° = 145°. Ex. 21. If two parallel lines are cut by a transversal, the sum of the two exterior angles on the same side of the transversal is equal to two right angles. Data : Two parallel lines, AB and CD, cut by the transversal EF in G and H respectively. To prove the...

...corresponding angles are equal. Corollary II. If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles. Corollary III. If a straight line is perpendicular to one...