Question: WEEK 1 MATHEMATICS - WRITTEN WORK 1 A. Write/Draw the correct relation symbol (>, ZM; MN + LM > N; ZM + IN > MIN

WEEK 1 MATHEMATICS - WRITTEN WORK 1 A. Write/Draw the correct relation symbol (>, ZM; MN + LM > N; ZM + IN > MIN Proof: Notice that since MN > IN and that MN > LM, then it is obvious that MN + LM > IN and MN + LN > LM are true. Hence, what remains to be proved is the third statement: LM + LN > MN Let us construct LP as an extension of ZM such that L is between M and P. LP & LN and A LMN is formed. MStatements Reasons 1. LP = IN 1. By construction 2. ALNP is an isosceles triangle. 2. 3. ZLNP & ZLPN 3. Base angles of isosceles triangles are congruent. 4. ZLPN & AMPN 4. 5. ZLNP & AMPN 5. 6. ZMNP * LLNM + LLNP 6. Angle Addition Postulate 7. 7. Substitution Property 8. ZMNP > ZMPN 8. Property of Inequality 9. MP > KIN 9. Triangle Inequality Theorem 2 (Aa-Sa) 10. IM + LP = MP 10. Segment Addition Postulate 11. 1 1. Substitution Property 12. IM + IN > MN 12

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