Algebra and Trigonometry Super Review (2nd Edition) (Super

REA's Algebra and Trigonometry great Review
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Extra resources for Algebra and Trigonometry Super Review (2nd Edition) (Super Reviews Study Guides)

Example text

To the sum of two right dihedral angles). 57. re dropp€d to its faces. Prove that the angle between the perpendiculars is congruent to the angle supplementary to the linear angle. 58. re perpendicular to t he faces of another trihedral angle. re perpendicular to the edges of the second. ch pair of dihedral angles is smaller than the sum of the t hird dihedral angle and 2d. e. than the angle sum of a convex n-gon). * One of two polyhedral angles with the same vertex lies inside the other. Prove that the sum of plane angles of the latter one is greater than the sum of plane angles of the former.

Compute the volume of a triangular pyramid all of whose lateral faces are perpendicular to each other and have areas a2, b2, and C2. 103. Compute the volume of a triangular pyramid, if each lateral edge makes the angle 45° with the base, whose sides are a, b, and c. * Compute t he volume of a triangular prism (possibly oblique) if the area of one of its lateral faces is S, and the distance from the plane of this face to the opposite edge is d. * Compute the volume of a right triangular prism whose base has the area 4 crn 2, and the lateral faces 9 cm 2, 10 cm2, and 18 cm 2.

Indeed, let S and S' (Figure 69) be two centers of homothety, and let A be any point of the given figure. Denote by B and B' the points obtained from A by the homothety with the same coefficient k with respect to the centers S and S' respectively. We will assume that k > 1. The case where k < 1 (including the negative values) is very similar and will be left to the reader as an exercise . In the triangles SAS' and BAB', which lie in the same plane, the angles at the vertex A are congruent (as vertical) , and the sides adjacent to the these angles are proportional.

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