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Discover Missing Sides in Triangles: Pythagorean Theorem & Solid Figures

Explore the relationship between 30, 60, 90 triangles and find missing sides using the Pythagorean Theorem. Delve into the properties of rectangular solids, cubes, and square pyramids with detailed diagrams and step-by-step solutions. Understand diagonals, faces, edges, vertices, altitudes, slant heights, and more.

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Discover Missing Sides in Triangles: Pythagorean Theorem & Solid Figures

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  1. Warm Up Use what you know about 30, 60, 90 triangles to find the missing sides!

  2. 9.8 Pythagorean Theorem and Space Figures

  3. 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

  4. Cube • A rectangular solid in which all edges are congruent. What is the diagonal of each side? 3 3 3

  5. 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.

  6. Look at the right angles inside and out.

  7. Look for the right angles here.

  8. Try this: find HB Keep your answer in reduced radical form.

  9. Two steps!

  10. Try one more 

  11. These are fun!

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