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Problem 241
Find the mean proportional between 4 and 16 .
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Prove that any two regular polygons with the same number of sides are similar.
Given; \(\underline{A D}\) is an angle bisector of \(\triangle \mathrm{ABC} ;\) point \(\mathrm{E}\) is on \(\underline{\mathrm{AD}}\) such that $\mathrm{AB} \cdot \mathrm{AC}=\mathrm{AD} \cdot \mathrm{AE}\(. Proves \)\phi \mathrm{B} \cong<\mathrm{AEC}$.
The lengths of two corresponding sides of two similar polygons are 4 and 7 . If the perimeter of the smaller polygon is 20 , find the perimeter of the larger polygon.
Given the A.A.A. (Angle, Angle, Angle) Similarity Theorem, prove the A.A. (Angle, Angle) Similarity Theorem.
Let \(\mathrm{ABC}\) be a triangle where \(\mathrm{D}\) is a point on \(\underline{\mathrm{AB}}\), and \(\mathrm{E}\) is a point on \(\underline{\mathrm{AC}}\). Prove that if $\underline{\mathrm{DE}} \| \underline{\mathrm{BC}}\(, then \)\mathrm{AB} / \mathrm{AD}=\mathrm{BC} / \mathrm{DE}$. (See figure.)
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