By Alfred S. Posamentier
Advanced Euclidean Geometry provides an intensive assessment of the necessities of high institution geometry after which expands these suggestions to complicated Euclidean geometry, to offer lecturers extra self assurance in guiding pupil explorations and questions.
The textual content includes enormous quantities of illustrations created within the Geometer's Sketchpad Dynamic Geometry® software program. it really is packaged with a CD-ROM containing over a hundred interactive sketches utilizing Sketchpad™ (assumes that the person has entry to the program).
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Extra resources for Advanced Euclidean Geometry
Prove that AW, RV, and CU are concurrent (at point K). 6. In AABC (Figure 2 - 1 ^ A^BM , and CN are concurrent at point K and I, My and N are points on BCy AC, and AB, respectively. Points P, R, and Q are respective midpoints of AL, CN, and BM. Prove that DP, BQ, and PP are con current if D, £, and P are respective midpoints of BC, AC, and AB. 7. In AABC (Figure 2-17), AL, BM, and CN are concurrent at point P Points S, Q, and R are midpoints of MN, ML, and NL, respectively. Prove that A S , BP, and CQ are concurrent.
A Because r > a and the square of a real number is positive, (r — > 0. This can be written as — 2ra + a " > 0 . Thus > 2ra. Multiplying both sides of this inequality by we get ^ ^----1- a j > r, which is ~(OR + OP) > r, or OM > r. This implies that point M must be outside the circle and that points S and T do not exist. ” I FALLACY 5 ^‘Q r o o f ’ Two segments of unequal length are actually of equal length. Consider AABCy with M N \ \ BC and MN intersecting AB and AC in points M and N, respectively (see Figure 1-^).
In AABC (Figure 2-15), AL, BM, and CN are concurrent at point P. Points Uy Vy and W are chosen on AJ5, AC, and BCy respectively, so that LU\\ AC, N V II BCy and MW' || AR. Prove that AW, RV, and CU are concurrent (at point K). 6. In AABC (Figure 2 - 1 ^ A^BM , and CN are concurrent at point K and I, My and N are points on BCy AC, and AB, respectively. Points P, R, and Q are respective midpoints of AL, CN, and BM. Prove that DP, BQ, and PP are con current if D, £, and P are respective midpoints of BC, AC, and AB.
Advanced Euclidean Geometry by Alfred S. Posamentier