...and a side of the one respectively equal to the hypotenuse and a side of the other. PROPOSITION XI. If two angles of a triangle are equal, the sides opposite to them are equal, and the triangle is isosceles. PROPOSITION XII. If two angles of a triangle are unequal,...

...and 4 or 5. i . From the greater of two given straight lines to cut off a part equal to the less. a. If two angles of a triangle are equal, the sides opposite to them shall also be equal. 3. In questions i and 2, we have representatives of two classes of propositions....

...HARVARD COLLEGE, September, 1891. In solving problems use fur JT the approximate value 31. 1. Prove that, if two angles of a triangle are equal, the sides opposite these angles are equal to each other. In a certain isosceles triangle ABC, A = B = 30°, and AC = 20...

...problem is solved. QED 4. Solve the same problem, using for the figure an acuteangled triangle. 5. Show that if two angles of a triangle are equal, the sides opposite those angles are equal, ie the triangle will be isosceles. 32. THEOREM. If two angles of a triangle...

...Prove that the side of a regular hexagon is equal to the radius of the circumscribed circle. 6 Prove that if two angles of a triangle are equal the sides opposite them are equal. 7 Given the base, one of the other sides and the altitude of a triangle, to construct...

...EXAMINATION, FOURTH CLASS, IN GEOMETRY, MARi и Ю, 1886. PART I — g to 9.30 am [Weight, 13.] 1. If two angles of a triangle are equal, the sides opposite to them are also equal. [Weight, 2.] 2. If from :i point without a circle a tangent and a secant are drawn,...

...seen that if two sides of a triangle are equal the angles opposite to them are equal. We have to prove that if two angles of a triangle are equal the sides opposite to them are equal. We employ "reductio ad absurdum." We assume as true the opposite of the fact that we...

...Eepeat Ex. 4G7 two or three times with other lines and angles. THEOREM 13. [CONVERSE OF PROPOSITION 12.] If two angles of a triangle are equal, the sides opposite to these angles are equal. Data ABC is a triangle which has L. B = LC To prove that AC = AB. Construction Draw AD to represent...

...the triangles into which the bisector of the vertical angle divides the isosceles triangle, THEOR. 8. If two angles of a triangle are equal, the sides opposite to those angles are equal Let ABC be a triangle having the angle ABC equal to the angle ACB : A A' B g...

...Spelling, and General Intelligence will be taken into account throughout the Examination. 1. Prove that if two angles of a triangle are equal the sides opposite to them are equal. 2. Prove that the three angles of any triangle are equal to two right angles. 3. Employ...