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Aim 3.8: How can we use CPCTC?

Do Now: Solve the following proof Given: AD bisects BC Angle BDA Angle CDA Prove: ABD ACD Homework: Page 15 #1 & 2 **Quiz Tomorrow**. A. Aim 3.8: How can we use CPCTC?. B. C. D. Statement Reason Angle J Angle L 1. Given B is the mdpt of JL 2. Given

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Aim 3.8: How can we use CPCTC?

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  1. Do Now: Solve the following proof Given: AD bisects BC Angle BDA Angle CDA Prove: ABD ACD Homework: Page 15 #1 & 2 **Quiz Tomorrow** A Aim 3.8: How can we use CPCTC? B C D

  2. Statement Reason Angle J Angle L 1. Given B is the mdpt of JL 2. Given JB BL 3. A mdpt cuts a line in ½ Angle JBH Angle CBL 4. Vertical Angles are JHB LCB 5. ASA Homework Answers: Aim 3.8: How can we use CPCTC?

  3. Given: AD is perpendicular to BC D is the midpoint of BC Prove: ABD ADC Proof #1: A B D C Aim 3.8: How can we use CPCTC?

  4. Statement Reason AD is perpendicular to BC 1. Given Angle ADB & ADC are 2. Perpendicular lines right angles form right angles 3. Angles ADB ADC 3. All right angles are 4. D is the mdpt of BC 4. Given 5. BD DC 5. A mdpt cuts a line in ½ 6. AD AD 6. Reflexive 7. ABD ADC 7. SAS Proof: Aim 3.8: How can we use CPCTC?

  5. Corresponding Parts of Congruent Triangles are Congruent: CPCTC • If we have already proved two triangles are congruent, then all of the other sides and angles in the two triangles are congruent as well. • We can use this to prove any sides or angles not used in the original proof to be congruent to each other. What is cpctc and what does it do? Aim 3.8: How can we use CPCTC?

  6. Given: AB CD AE DE Prove: BE CE Example: E A B C D Aim 3.8: How can we use CPCTC?

  7. Given: AB DE AE bisects BD Prove: AB DE Example: A B C D E

  8. Statement Reason AB is parallel to DE 1. Given Angle A Angle E 2. When lines are parallel, alternate interior angles are AE bisects BD 3. Given DC CB 4. A bisector cuts a line ½ Angle ACB Angle DCB 5. Vertical angles are ACB DCE 6. ASA AB DE 7. CPCTC Proof: Aim 3.8: How can we use CPCTC?

  9. Given: NT ST YT bisects angle NTS Prove: Angle N Angle S Your turn! N 1 Y T 2 S Aim 3.8: How can we use CPCTC?

  10. Statement Reason NT ST 1. Given YT bisects angle NTS 2. Given Angle 1 Angle 2 3. A bisector cuts an angle in ½ YT YT 4. Reflexive property NTY STY 5. SAS Angle N Angle S 6. CPCTC Proof: Aim 3.8: How can we use CPCTC?

  11. Given: FH FI FS bisects HI Prove: Angle HFS Angle IFS F Example: H I S Aim 3.8: How can we use CPCTC?

  12. Statement Reason FH FI 1. Given FH bisects HI 2. Given HS IS 3. A bisector cuts a side in ½ FS FS 5. Reflexive Property FSH FSI 6. SSS Angle HFS Angle IFS 7. CPCTC Proof Aim 3.8: How can we use CPCTC?

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