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NOTE: Please do not copy paste already existing answers. Q) Q) Prove the Converse to the Similar Triangles Theorem (Theorem 5.3.4) Theorem 5.3.4 (Converse to Similar Triangles Theorem). If△ABC and △D...
2) (i) State the converse of the Alternate Interior Angle Theorem in Neutral Geometry. (ii) Prove that if the converse of the Alternate Interior Angle Theorem is true, then all triangles have zero defect. [Hint: For an arbitrary triangle, ABC, draw a line through C parallel to side AB. Justify why you can do this.] 5) Consider the following statements: I: If two triangles are congruent, then they have equal defect. II: If two triangles are similar, then they have...
4. (a) Supply proof of the Menelaus Theorem concerning a transversal line L cutting the sides of ΔABC at points X,Y,Z respectively. (Hint) Drop perpendicular line segments from A, B, C to L and use similar triangles b)Centuries after Menelaus, Ceva discovered the Theorem that if P,Q, R are points on BC, CA and AB respectively so that AP, BQ, CR meet at a single point K, thern AR BP co RB PC QA Prove Ceva's theorem and its converse,...
Moment for Discovery SSS Theorem Via Kites and Darts Two geometric figures, the kite and dart, though elementary, are quite useful. The figures we have in mind are shown in Figure 3.26, where it is assumed that AB = AD and BC = CD. The dart is distinguished from the kite by virtue of the eight angles at A, B, C, and D involving the diagonals AC and BD being either all acute angles (for the kite), or two of...