1 / 10

CPCTC

L. _____  _____. J. N. K. M. CPCTC. Be able to use CPCTC to find unknowns in congruent triangles!. Quick Review. Are these triangles congruent? By which postulate/theorem?. Oh, and what is the Reflexive Property again?.

shana
Download Presentation

CPCTC

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. L _____  _____ J N K M CPCTC Be able to use CPCTC to find unknowns in congruent triangles! Quick Review Are these triangles congruent? By which postulate/theorem? Oh, and what is the Reflexive Property again? It says something is equal to itself. EX: A  A or AB  AB.

  2. C.P.C.T.C. Corresponding Parts of Congruent Triangles are CONGRUENT!! CPCTC Once you have shown triangles are congruent, then you can make some CONCLUSIONS about all of the corresponding parts (_______ and __________) of those triangles! sides angles

  3. B Y Z C X A Are the triangles congruent? By which postulate or theorem? Yes; ASA What other parts of the triangles are congruent by CPCTC? If B = 3x and Y = 5x –9, find x. BY 3x = 5x - 9 9 = 2x AB  ZY BC  YX

  4. C L 3 4 1 2 R S 1. 1. ___________ 3. 3. ___________ PROOFS! Given: Prove: Given 2. _______________ 2. Reflexive SAS CPCTC 4. _______________ 4. ___________

  5. C V Given: R H A E Prove: 1. _____________________ 1. Given 2. _____________________ 2. SSS CPCTC 3. _____________________ 3. ________

  6. R C Q Y P T State why the two triangles are congruent and write the congruence statement. Also list the other pairs of parts that are congruent by CPCTC. YQ CT  RP CY  RP AAS

  7. 40 yd 30 yd 24.5 yd 30 yd 40 yd A geometry class is trying to find the distance across a small lake. The distances they measured are shown in the diagram. Explain how to use their measurements to find the distance across the lake. Vertical angles are congruent. The triangles are congruent by SAS. The width of the lake has to be 24.5 yd by CPCTC.

  8. A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond. What is JK? • One angle pair is congruent, because they are vertical angles. • Two pairs of sides are congruent, because their lengths are equal. • Therefore the two triangles are congruent by SAS. • By CPCTC, the third side pair is congruent, so JK = 41 ft.

  9. 1. N  P; NO || MP Given: NO || MP, N P Prove: MN || OP 3. MO  MO 6. MN || OP Statements Reasons 1. Given 2. NOM  PMO 2. Alt. Int. s Thm. 3. Reflex. Prop. of  4. ∆MNO  ∆OPM 4. AAS 5. NMO  POM 5. CPCTC 6. Conv. Of Alt. Int. s Thm.

  10. 6. DX  BX Given: X is the midpoint of AC . 1 2 Prove: X is the midpoint of BD. Statements Reasons 1. X is mdpt. of AC. 1  2 1. Given 2. AX = CX 2. Def. of mdpt. 3. AX  CX 3. Def of  4. AXD  CXB 4. Vert. s Thm. 5. ∆AXD  ∆CXB 5. ASA Steps 1, 4, 5 6. CPCTC 7. Def. of  7. DX = BX 8. X is mdpt. of BD. 8. Def. of mdpt.

More Related