Plane And Solid Geometry, Suggestive Method
Plane And Solid Geometry, Suggestive Method
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Theorem. // two trihedral angles have the three face angles of one eqiml respectively to the three face angles of the other ^ and arranged in the same order J the trihedral angles are equal in all respects.
A Let A and A' represent two trihedral angles In which ZBAC=B' A'C, ZCAD=C' A' D',and ZBAD= B'A' D\ etc., the angles being ^arranged in the same order.
To prove that trihedral angle A is equal to trihedral angle A'.
Suggestion i. Place thl. ^ A upon thl. ^ A' with line ^ 5 in .4' B' and face... ABC lying in the plane ofA'B' C, where does line i4 C lie ? Why ?
2. Where does plane A C D ]ie {^ 475) ? Where does Une A D ]ie with respect to i4' 2?' ? Why ?
5. Where does plane B A D ]ie? Why ?
Therefore — Ex. 305. If two planes are cut by a third plane so that the corresponding dihedral angles are equal and the edges of the dihedral angles formed are parallel, the two planes are parallel. Fig. Ex. 299.
26o SOLID GEOMETRY.
Proposition XXXVII.
477. Theorem. Two symmetrical isosceles trihe- dral angles are eqtial in all respects.
What to read after Plane And Solid Geometry, Suggestive Method?
You can find similar books in the "Read Also" column, or choose other free books by George C George Clinton Shutts to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Theorem. // two trihedral angles have the three face angles of one eqiml respectively to the three face angles of the other ^ and arranged in the same order J the trihedral angles are equal in all respects.
A Let A and A' represent two trihedral angles In which ZBAC=B' A'C, ZCAD=C' A' D',and ZBAD= B'A' D\ etc., the angles being ^arranged in the same order.
To prove that trihedral angle A is equal to trihedral angle A'.
Suggestion i. Place thl. ^ A upon thl. ^ A' with line ^ 5 in .4' B' and face... ABC lying in the plane ofA'B' C, where does line i4 C lie ? Why ?
2. Where does plane A C D ]ie {^ 475) ? Where does Une A D ]ie with respect to i4' 2?' ? Why ?
5. Where does plane B A D ]ie? Why ?
Therefore — Ex. 305. If two planes are cut by a third plane so that the corresponding dihedral angles are equal and the edges of the dihedral angles formed are parallel, the two planes are parallel. Fig. Ex. 299.
26o SOLID GEOMETRY.
Proposition XXXVII.
477. Theorem. Two symmetrical isosceles trihe- dral angles are eqtial in all respects.
What to read after Plane And Solid Geometry, Suggestive Method?
You can find similar books in the "Read Also" column, or choose other free books by George C George Clinton Shutts to read onlineMoreLess
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