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Aim 3.12: To Use CPCTC to Prove Other Things

Aim 3.12: To Use CPCTC to Prove Other Things. Do Now: Solve the following proof: Given: AB AD BC CD Prove: Angle B Angle D Homework: Packet Page 17 #1 & #2. A. B. D. C. Aim 3.12: To Use CPCTC to Prove Other Things. Example:. Given: AD is perpendicular to BC

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Aim 3.12: To Use CPCTC to Prove Other Things

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  1. Aim 3.12: To Use CPCTC to Prove Other Things Do Now: Solve the following proof: Given: AB AD BC CD Prove: Angle B Angle D Homework: Packet Page 17 #1 & #2 A B D C

  2. Aim 3.12: To Use CPCTC to Prove Other Things Example: Given: AD is perpendicular to BC Triangle ABC is Isosceles Prove: AD bisects BC A B C D

  3. What Do We Need? ? ? • Parallel Lines? Congruent Alternate Interior Angles • Isosceles Triangle? A Pair of Congruent Sides & Angles • Side or Angle Bisector? Two Congruent Sides or Angles that make up a larger side or angle • Midpoint? A pair of congruent sides ? ? Aim 3.12: To Use CPCTC to Prove Other Things

  4. Aim 3.12: To Use CPCTC to Prove Other Things Example: Given: A is the midpoint of GT and IN Prove: GI NT G N A I T

  5. Aim 3.12: To Use CPCTC to Prove Other Things Example: Given: JT is perpendicular to ES Angle E Angle S Prove: JT bisects ES J E S T

  6. Aim 3.12: To Use CPCTC to Prove Other Things Proof: Statement Reason • JT is perpendicular to ES 1. Given • Angle ETJ & STJ are 2. Perpendicular lines right angles form right angles • Angle ETJ Angle STJ 3. All right angles are = • Angle E Angle S 4. Given • JT JT 5. Reflexive Property • ETJ STJ 6. AAS • ET ST 7. CPCTC • JT bisects ES 8. Two sides show a bisector cuts a line in ½

  7. Aim 3.12: To Use CPCTC to Prove Other Things Example: Given: HI HE HK bisects IE Prove: HK bisects Angle IHE H I E K

  8. Aim 3.12: To Use CPCTC to Prove Other Things Proof: Statement Reason • HI HE 1. Given • HK bisects IE 2. Given • IK KE 3. A bisector cuts a side in ½ • HK HK 4. Reflexive Property • IHK EKH 5. SSS • Angle IHK Angle EHK 6. CPCTC • HK bisects Angle IHE 7. Two angles show a bisector cuts an angle in ½

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