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Pythagorean Theorem and Space Figures

This lesson covers the Pythagorean theorem and various space figures such as rectangular solids and regular square pyramids. It explains concepts like faces, edges, vertices, diagonals, altitudes, slant heights, and right angles.

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Pythagorean Theorem and Space Figures

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  1. Pythagorean Theorem and Space Figures Lesson 9.8

  2. Rectangular Solid • Face • Edge AB is one of 12 edges • Diagonal HB is one of 4 diagonals ABFE is one rectangular face out of the 6 faces H G E F O C A B

  3. Regular Square Pyramid • Square base Bottom of the pyramid. • Vertex • Altitude • Slant height Point where the edges of the triangles meet. Distance from vertex to the base. It is perpendicular to the center of the base. Height of the triangles, perpendicular to the base of the triangle.

  4. Look at the right angles inside and out.

  5. Look for the right angles here.

  6. Find HB Keep your answer in reduced radical form. ΔABD, 32 + 72 = (BD)2 √58 = BD ΔHDB, 52 + (√58)2 = (HB)2 25 + 58 = (HB) 2 √83 = HB

  7. JK = ¼ of JKMO = ¼ (40) = 10 • The slant height of the pyramid is the perpendicular bisector of MK, so PSK is a right Δ. • (SK)2 + (PS)2 = (PK)2 • 52 + (PS)2 = 132 • PS = 12 C. The altitude of a regular pyramid is perpendicular to the base at its center. Thus, RS = ½ (JK) = 5, and PRS is a right Δ. (RS)2 + (PR)2 = (PS)2 52 + (PR)2 = 122 PR = √119

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