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Download Saccheri Quadrilaterals in Neutral Geometry E D A C B
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Saccheri Quadrilaterals in Neutral Geometry € A Saccheri Quadrilateral is a quadrilateral with congruent opposite sides that are both perpendicular to the base. Quad ABCD is a Saccheri Quadrilatreal. We call BC the base, AD the summit, and angles ∠BAD and ∠CDA the summit angles. A D € € € B C First, show the following two results in neutral (absolute) geometry: 1. The diagonals of a Saccheri Quadrilateral are congruent. 2. The summit angles of a Saccheri Quadrilateral are congruent. Here are several more results related to Saccheri Quadrilaterals. Try to come up with a way to justify each of the following results: 3. The line joining the midpoints of the summit and base of a Saccheri Quadrilateral is perpendicular to both the summit and base. 4. The angle sum of a triangle ( ΔAED ) is equal to the sum of the summit angles of its associated Saccheri Quadrilateral. A D € B C E 5. The summit angles of a Saccheri Quadrilateral are each less than or equal to 90 degrees. (Hint: Use the result from #4 above.)
