Beginning Proofs Task Cards
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1 eginning Proofs Task ards NSWR KY. Given: and are complementary; m = 74 Prove: m = 6. and are complementary. Given. m + m = 90. efinition of omplementary ngles. m = 74. Given 4. m + 74 = Substitution Property of quality (,) 5. m = 6 5. Subtraction Property of quality. Given: HI = 9 ; IJ = 9 ; IJ JH H I Prove: HI JH. HI = 9. Given. IJ = 9. Given. HI = IJ. Transitive Property of quality (,) 4. HI IJ 4. efinition of ongruent Segments 5. IJ JH 5. Given 6. HI JH 6. Transitive Property of ongruence (4,5) J. Given: and are supplementary and are supplementary Prove:. and are supplementary. Given. m + m = 80. efinition of Supplementary ngles. and are supplementary. Given 4. m + m = efinition of Supplementary ngles 5. m + m = m + m 5. Transitive Property of quality (,4) 6. m = m 6. Subtraction Property of quality efinition of ongruent ngles
2 4. Given: and are supplementary; m = 45 Prove: m = 5. and are supplementary. Given. m + m = 80. efinition of Supplementary ngles. m = 45. Given 4. m + 45 = Substitution Property of quality (,) 5. m = 5 5. Subtraction Property of quality 5. Given: M is the midpoint of ; is the midpoint of M Prove: M = M M. M is the midpoint of. Given. is the midpoint of M. Given. M M and M. efinition of Midpoint 4. M = M and M = 4. efinition of ongruent Segments 5. M = M + 5. Segment ddition Postulate 6. M = M + M 6. Substitution Property of quality (4,5) 7. M = M 7. ombine Like Terms (istributive Property) 6. Given: and are complementary; m + m = 90 Prove:. and are complementary. Given. m + m = 90. efinition of omplementary ngles. m + m = 90. Given 4. m + m = m + m 4. Transitive Property of quality (,) 5. m = m 5. Subtraction Property of quality efinition of ongruent ngles
3 7. Given: ; m = m Prove: m + m = 90.. Given. is a right angle. efinition of Perpendicular Lines. m = 90. efinition of Right ngle 4. m = m + m 4. ngle ddition Postulate 5. m + m = Transitive Property of quality (,4) 6. m = m 6. Given 7. m + m = Substitution Property of quality (5,6) 8. Given: m X = m X ; m = m Prove: m = m 4. m X = m X. Given X 4. m X = m + m. ngle ddition Postulate. m X = m + m 4. ngle ddition Postulate 4. m + m = m + m 4 4. Substitution Property of quality (,,) 5. m = m 5. Given 6. m + m = m + m 4 6. Substitution Property of quality (4,5) 7. m = m 4 7. Subtraction Property of quality 9. Given: = ; = Prove: =. = and =. Given. + = +. ddition Property of quality. + = +. Substitution Property of quality (,) 4. + = 4. Segment ddition Postulate 5. + = 5. Segment ddition Postulate 6. = 6. Substitution Property of quality (,4,5)
4 0. Given: = Prove: =. =. Given. = +. Segment ddition Postulate. = +. Substitution Property of quality (,) 4. = 4. Subtraction Property of quality 5. = 5. ombining Like Terms (istributive Property)!!!". Given: bisects Prove: m = m!!!". bisects. Given.. efinition of ngle isector. m = m. efinition of ongruent ngles 4. m + m = m 4. ngle ddition Postulate 5. m + m = m 5. Substitution Property of quality (,4) 6. m = m 6. ombining Like Terms (istributive Property) 7. m = m 7. ivision Property of quality. Given: L = SK Prove: S = LK. L = SK. Given L S. LS = LS. Reflexive Property of quality. L + LS = SK + LS. ddition Property of quality 4. L + LS = S 4. Segment ddition Postulate 5. SK + LS = LK 5. Segment ddition Postulate 6. S = LK 6. Substitution Property of quality (,4,5) K
5 . Given: ; Prove:. ;. Given. = ; =. efinition of ongruent Segments. = +. Segment ddition Postulate 4. = + 4. Substitution Property of quality 5. = + 5. Segment ddition Postulate 6. + = + 6. Transitive Property of quality (4,5) 7. = 7. Subtraction Property of quality efinition of ongruent Segments H 4. Given: HI TU and HJ TV I T U V Prove: IJ UV J. HI TU and HJ TV. Given. HI = TU and HJ=TV. efinition of ongruent Segments. HI + IJ = HJ. Segment ddition Postulate 4. TU + IJ = TV 4. Substitution Property of quality (,) 5. TU +UV = TV 5. Segment ddition Postulate 6. TU + IJ = TU +UV 6. Transitive Property of quality (4,5) 7. TU = TU 7. Reflexive Property of quality 8. IJ = UV 8. Subtraction Property of quality 9. IJ UV 9. efinition of ongruent Segments
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