By Francis J. Grund
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Additional resources for An elementary treatise on geometry : simplified for beginners not versed in algebra. Part I, containing plane geometry, with its application to the solution of problems
Wlien two angles of a triangle are equal 3. to two angles of another triangle, the third angle in the one equal 4. 5. 6. to the third is angle in the other. No triangle can contain more than one right angle. No triangle can contain more than one obtuse angle. No triangle can contain a right and an obtuse angle together. 7. to the Q. In a right-angled sum of the two How triangle, the right angle can you convince these assertions is equal other angles. me of the truth of each of ? OF THE TRUTHS CONTAINED THE FIRST SECTION.
ABD con- ; and the third equal to the third side but one point in the line 3/N, on tacJi the point snch, A, is that a strmglit line, of a given length. This 4. but ene point in the line is the peipendicidar , in of ; 1, Sect. ) pa'pendicultstr, of the side triangle, is (Query h Tltere 6thly. side one in the the other. are equal which a MN, on each line draicn to the MN A an angle of a given forms with the line magnitude. This follows from No. 3. point QUERY If two and sides, X. the angle which is opposite greater of them, in one triangle, are equal to which the angle is the and opposite to the greater of than in each to each, what relation do these two anoilier, gles bear to each other A.
Can you now find JB out the relation which the exterior angle e bears to the two interior angles and b? A. The e is a ^L exterior angle equal to the :>um of the two interior angles^ a and * The teacher by may c to the two angles a give his pupils an ocular demonstration of cutting the three angles 6, d, e, then placing them along side of each other Btraight line. ^ b. Q. How can you prove this ? A. Because, by adding the angle this truth, ^ Jl from a triangle, and ; they will be in a ^t GEOMETRY.
An elementary treatise on geometry : simplified for beginners not versed in algebra. Part I, containing plane geometry, with its application to the solution of problems by Francis J. Grund