\fGiven: FD = FE Given: m/JKL = 350, mZGHE + mZFDE = 180 mLL = 100, Prove: AGFH ~ ADFE m/M = 450 I Prove: AJKL ~ AMKN Statements Reasons Statements 1. FD = FE 1 . Given Reasons 1 . m/JKL = 350, m/L= 100. MLM = 450 2. AFDE is isosceles 2. Definition of Isosceles Triangles 2. mLL + m/J+ m/JKL=180 3. mLGHE + mZFDE = 180 Given 3. 100 + m/J+ 350= 180 4. LFDE ~ LFED 4. Base Angles of an Isosceles Triangle are Congruent 5. mLFDE = mZFED 4. mLJ + 1350 =180 4. Simplify 6. m/GHE + m/FED = 180 5. mLJ = 450 5.Subtraction Property LGHE and LFED N are supplementary L's . Def at sup angles 6. mLJ =m/M 8. GH || DE 8 Consecutive Interior Angles Converse 7. LJ = LM N 9. LFHG = LFED 8. LJKL = LMKN 8, Vertical Angles Th 10. LGFH = LDFE 9. AJKL ~ AMKN a I 11. AGFH ~ ADFE Gina Wilson (All Things\f\fHelp Segment Division Property |Angle Addition Given Postulate Addition Postulate Addition Corresponding Substitution Definition of Angles of Similar Congruent Property Triangles are I Congruent SSS Similarity Vertical Angles Subtraction Corresponding Theorem Theorem Property Sides of Similar Triangles are Proportional AA Similarity Alternate Interior Reflexive Definition of Theorem Angles Theorem Property Supplementary Angles SAS Similarity Corresponding Definition of Linear Pair Theorem Angles Postulate Isosceles Theorem Triangle Definition of an Cross Product Definition of Angle Bisector Triangle Sum Property Midpoint Theorem Congruent Definition of a Supplements Right Angle Theorem C % U 6