...angles of a triangle are together greater than two right angles. 5. Show that only one perpendicular can be drawn to a given straight line from a given point without it. 6. Prove Euclid's Proposition XVII. without producing any side, but using a straight line...

...straight line that meets it in the plane A OB '. Therefore PO is perpendicular to the plane A OB. COR. 1. Of all the straight lines that can be drawn to a given plane from a given point, the shortest is the perpendicular ; and of the others those whose extremities...

...unequal.' This is the obverse of Prop. 6, and is an immediate inference from Prop. 5. Ex. 24. — Of all straight lines that can be drawn to a given straight...point outside it, the perpendicular is the shortest ; and of the others those which make equal angles with the perpendicular are equal; and that which...

...of BC then /ADB shall be obtuse. § 8. (Bookwork, EUCLID, I. 1.26.) 1. Of all straight lines which can be drawn to a given straight line from a given point outside, the perpendicular is the least ; and, of the others, those which make equal angles with the perpendicular...

...angles are complementary. XVII. 1. Prove by the method of superposition that only one perpendicular can be drawn to a given straight line from a given point without it. 2. BAC and BDC are two triangles on the same base BC and on the same side of it, and the...

...and is equal to the angle ACD, is greater than the angle ABC. EXERCISES. 1. Only one perpendicular can be drawn to a given straight line from a given point without it. 2. Shew by joining the angular point A of a triangle to any point in the opposite side...

...all the others are right angles. 3. Prove by the method of superposition that only one perpendicular can be drawn to a given straight line from a given point without it. 4. Prove by the method of superposition that, if two rightangled triangles have their hypotenuses...

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...AB (see fig. 144); from O draw six or seven straight lines to meet AB. Measure all these lines. GS THEOREM 21. Of all the straight lines that can be...point outside it, the perpendicular is the shortest. fig. 144. Data AB is a straight line and O a point outside it ; ON is drawn J. to AB meeting it at...

...the triangle ABC, the sum of OA, OB, and OC is less than the perimeter of the triangle. THEOE. 15. Of all the straight lines that can be drawn to a given...point outside it, the perpendicular is the shortest ; and of the others, those which make equal angles with the perpendicular are equal ; and that which...