...the circumferences, have the same ratio which the arcs on which they stand have to one another. 5. If two straight lines be at right angles to the same plane they shall be parallel to one another. II. — 1. Define the Trigonometrical Ratios and prove the relation sin2 A + cos2 A = 1. 2. Prove that...

...proportional between two given straight lines. 2. When is a straight line at right angles to a plane ? If two straight lines be at right angles to the same plane, they shall be parallel to one another. 3. Solve the equations — 4. Determine the arithmetical progression wherein the sum of ;i terms is...

...contained by the segments of the base together with the square of the line which bisects the angle. 11. If two straight lines be at right angles to the same plane they shall be parallel to one another. 12. If two parallel planes be cut by another plane their common sections with it are parallel. PROBLEMS....

...in numbers. 3. The difference between any number, and thatr number inverted, is divisible by 9. 4. If two straight lines be at right angles to the same plane, they are parallel to one another. 5. Given two sides and the included angle of a plane triangle : find the...

...joined and produced to meet DE and DF respectively in R and Q ; prove that AP, BQ, OR are parallel. 11. If two straight lines be at right angles to the same plane, they are parallel to each other. What is the shortest distance from a given point to a plane ; and why ?...

...intersect AB at a point different from O. In either case, an absurdity would result. PROPOSITION 6. If two straight lines be at right angles to the same plane, the straight lines will be parallel. For let the two straight lines AB, CD be at right angles to the...