Right Prism with a Square Lateral Face

Problem

In the right triangular prism $ABC$ - $A_1B_1C_1$ shown in the figure, $AB=AC=5$ , and the quadrilateral $B_1BCC_1$ is a square of side length $6$ . Points $D$ and $E$ are the midpoints of $BC$ and $BB_1$ respectively.

1. Prove that $A_1B \parallel$ plane $AC_1D$ .

2. Prove that $CE \perp$ plane $AC_1D$ .

3. Find the cosine of the dihedral angle $C$ - $AC_1$ - $D$ .

Answer

Solution

Difficulty	5/10
Topics	solid geometry, Triangle Geometry

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