Questions Answers Ch 5

30. Given: BD bisects ∠ADC BD ⊥ AC Prove: △ABD ≅ △CBD Statement Reason BD bisects ∠ADC given ∠ABD = ∠BDC definition of angle bisector BD ⊥ AC given ∠ABD = 90° def of perpendicular ∠CBD = 90° def of perpendicular ∠ABD = ∠CBD Substitution BD ≅ BD reflexive △ABD ≅ △CBD by ASA Draw separate △ to help you see or write this way 30. Given: BD bisects ∠ADC BD ⊥ AC Prove: △ABD ≅ △CBD Statement Reason BD ⊥ AC given ∠ABD = 90° def of perpendicular ∠CBD = 90° def of perpendicular ∠ABD = ∠CBD Transitive (both = 90°) BD ≅ BD Symmetric BD bisects ∠ADC given ∠ADB = ∠BDC def. of angle bisector △ABD ≅ △CBD by ASA I always check the picture to see if matches your statement or write this way 30. Given: BD bisects ∠ADC BD ⊥ AC Prove: △ABD ≅ △CBD Statement Reason BD bisects ∠ADC given ∠ADB = ∠BDC definition of angle bisector BD ⊥ AC given ∠ABD = 90° def of perpendicular ∠CBD = 90° def of perpendicular ∠ABD = ∠CBD transitive property BD ≅ BD Symmetric △ABD ≅ △CBD by ASA So many ways to write a proof! 31. Given: PS ≅ RS SQ ⊥ PR Prove: △PSQ ≅ △RSQ Statement Reason PS ≅ RS given SQ ⊥ PR given ∠PSQ = 90° def. of perpendicular ∠RSQ = 90° def. of perpendicular QS ≅ QS reflexive △PSQ is a right triangle definition of right triangle △RSQ is a right triangle definition of right triangle △PSQ ≅ △RSQ by HL or write like this 31. Given: PS ≅ RS SQ ⊥ PR Prove: △PSQ ≅ △RSQ Statement Reason QS ≅ QS reflexive PS ≅ RS given SQ ⊥ PR given ∠PSQ = 90° def. of perpendicular ∠RSQ = 90° def. of perpendicular △SQR is a right triangle def of right triangle △SQR is a right triangle def of right triangle △PSQ ≅ △RSQ by HL or another way 31. Given: PS ≅ RS SQ ⊥ PR Prove: △PSQ ≅ △RSQ Statement Reason SQ ⊥ PR given PS ≅ RS given QS ≅ QS symmetric (based on how you write) ∠PSQ = 90° def. of perpendicular ∠RSQ = 90° def. of perpendicular △SQR is a right triangle def of right triangle △SQR is a right triangle def of right triangle △PSQ ≅ △RSQ by HL #keep in mind which steps have to come before others