Plane and solid geometry . Given two dihedral A BC and Bc whose plane A MNO andMno are equal. To prove dihedral A BC = dihedral Z b&. Argument 1. Place dihedral A BC upon dihedral A bc so that plane A MNO shall besuperposed upon its equal, planeAmno\ 2. Then BC and B^c* are both ± MN and NO at N. 3. .-. BC and Bc are both ± plane 3fN0 at N, 4. .-. BC and Bc are collinear. 5. .*. planes AB and ab, determined by MN and BCy are coplanar; also planesCD and Ci), determined by BC andJVO, are eo])lanar. 6. .-. dihedral A BC = dihedral A Bc. J Reasons1. § 54, 14. 2. § 670. 3. § 622. 4. § 638. 5

---

Plane and solid geometry . Given two dihedral A BC and Bc whose plane A MNO andMno are equal. To prove dihedral A BC = dihedral Z b&. Argument 1. Place dihedral A BC upon dihedral A bc so that plane A MNO shall besuperposed upon its equal, planeAmno\ 2. Then BC and B^c* are both ± MN and NO at N. 3. .-. BC and Bc are both ± plane 3fN0 at N, 4. .-. BC and Bc are collinear. 5. .*. planes AB and ab, determined by MN and BCy are coplanar; also planesCD and Ci), determined by BC andJVO, are eo])lanar. 6. .-. dihedral A BC = dihedral A Bc. J Reasons1. § 54, 14. 2. § 670. 3. § 622. 4. § 638. 5. § 612. 6. § 18. BOOK VI 327 677. Cor. If the plane angle of a dihedral angle is aright angle, the dihedral angle is a right dihedralangle. Ex. 1199. Prove Ex. 1194 by applying § 676. Ex. 1200. If two parallel planes are cut by a transversal plane, thealternate interior dihedral angles are equal. Hint. Let ZABG be the plane Z of v dihedral Z V-WX-Y. Let the plane y/jf determined by AB and BC intersect plane f

---

Size: 1478px × 1690px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No

Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912