...intersect, the vertical angles are equal. 85. In congruent figures homologous parts are equal. 86. Any side of a triangle is less than the sum of the other two, and greater than their difference. 91. Two triangles are congruent if they have two sides and the included...

...equal angles are equal. [*] 12. The bisectors of vertical angles lie in a straight line. [J4-] 13. Any side of a triangle is less than the sum of the other two and greater than their difference. [*] 14. A diameter bisects a circle. [As.] 15. A straight line intersects...

...equal angles are equal. [*] 12. The bisectors of vertical angles lie in a straight line. \J4-] 13. Any side of a triangle is less than the sum of the other two and greater than their difference. [*] 14. A diameter bisects a circle. [As.] 15. A straight line intersects...

...to x; the sum of any two angles of a triangle is greater than the third angle, therefore any angle of a triangle is less than the sum of the other two angles. PRACTICE ON SECTIONS 16 and 17 Using any of the examples for practice in the preceding section,...

...an arithmetical example for each of the axioms. 159. Fundamental Inequalities for Segments. (a) Any side of a triangle is less than the sum of the other two sides. This follows from Ax. 11, §51. T\msBC<AB+AC. (6) Any side of a triangle is greater than the...

...an arithmetical example for each of the axioms. 159. Fundamental Inequalities for Segments. (a) Any side of a triangle is less than the sum of the other two sides. (6) Any side of a triangle is greater than the difference between the other two sides. Thus,...

...is the line segment Joining the points, (4) Two distinct points determine a straight line, (5) Any side of a triangle is less than the sum of the other two sides, (6) A diameter bisects a circle, (7) A straight line intersects a circle at most in two points,...

...other two sides, will the angle opposite the first side be acute or obtuse ? Ex. 3. If the square on one side of a triangle is less than the sum of the squares on the other two sides, will the angle opposite the first side be acute or obtuse? Ex. 4. Is...

...is the line segment joining the points, (4) Two distinct points determine a straight line, (5) Any side of a triangle is less than the sum of the other two sides, (6) A diameter bisects a circle, (7) A straight line intersects a circle at most in two points,...

...are unequal and bisect each other at right angles, the figure is a rhombus. 146. Postulate VI. Any side of a triangle is less than the sum of the other two sides. A still broader and more usual statement is: A straight line is the shortest line between two...