Question: fC. Directions: Complete the two-column proof. (10-15) Given: A LMN where IM ZM; MN + LM > IN; ZM + IN > MIN Proof: Notice

\fC. Directions: Complete the two-column proof. (10-15) Given: A LMN where IM ZM; MN + LM > IN; ZM + IN > MIN Proof: Notice that since MN > IN and that MN > IM, then it is obvious that MN + ZM > IN and MN + IN > ZM 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. IP . IN and A LMN is formed. 2 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 ~ ZLNM + ZLNP 6. Angle Addition Postulate 7. 7. Substitution Property 8. ZMNP > ZMPN 8. Property of Inequality 9. MP > MN 9. Triangle Inequality Theorem 2 (Aa-Sa) 10. LM + LP = MP 10. Segment Addition Postulate 11. 1 1. Substitution Property 12. ZM + IN > MN 12

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