CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT Section

  • Slides: 14
Download presentation
CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT Section 4 -6 Geometry Pre. AP, Revised

CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT Section 4 -6 Geometry Pre. AP, Revised © 2013 viet. dang@humble. k 12. tx. us 12/28/2021 3: 16 PM 4 -6: CPCTC 1

12/28/2021 3: 16 PM 4 -6: CPCTC 2

12/28/2021 3: 16 PM 4 -6: CPCTC 2

DEFINITIONS A. Recall that an angle bisector is a ray that divides the angle

DEFINITIONS A. Recall that an angle bisector is a ray that divides the angle into two congruent parts. B. Two triangles are congruent triangles if and only if the Corresponding Parts of Congruent Triangles are Congruent, known as CPCTC. C. Remember, first show that the triangles are congruent with a shortcut, then use CPCTC to show the segments are congruent. D. Segments and Angles present CPCTC. E. If two triangles are congruent, then all of their corresponding parts are congruent. F. You can only use CPCTC after you know that two triangles are congruent. 12/28/2021 3: 16 PM 4 -6: CPCTC 3

EXAMPLE 1 Identify a triangle in the figure that appears to be congruent to

EXAMPLE 1 Identify a triangle in the figure that appears to be congruent to the given triangle. 1) ΔATB 2) ΔTAO 3) ΔOVB 12/28/2021 3: 16 PM 4 -6: CPCTC 4

YOUR TURN Identify a triangle in the figure that appears to be congruent to

YOUR TURN Identify a triangle in the figure that appears to be congruent to the given triangle. 1) ΔYUM 2) ΔWYU 3) ΔMTY 12/28/2021 3: 16 PM 4 -6: CPCTC 5

EXAMPLE 2 Explain why ∆CAD ∆BAD. 12/28/2021 3: 16 PM 4 -6: CPCTC 6

EXAMPLE 2 Explain why ∆CAD ∆BAD. 12/28/2021 3: 16 PM 4 -6: CPCTC 6

EXAMPLE 3 Z 12/28/2021 3: 16 PM 4 -6: CPCTC 7

EXAMPLE 3 Z 12/28/2021 3: 16 PM 4 -6: CPCTC 7

YOUR TURN 12/28/2021 3: 16 PM 4 -6: CPCTC 8

YOUR TURN 12/28/2021 3: 16 PM 4 -6: CPCTC 8

EXAMPLE 4 X Statements Reasons Given Reflexive Property SAS CPCTC 12/28/2021 3: 16 PM

EXAMPLE 4 X Statements Reasons Given Reflexive Property SAS CPCTC 12/28/2021 3: 16 PM 4 -6: CPCTC 9

EXAMPLE 5 Statements Reasons Given Definition of Bisector Given Third Angle Theorem ASA CPCTC

EXAMPLE 5 Statements Reasons Given Definition of Bisector Given Third Angle Theorem ASA CPCTC 12/28/2021 3: 16 PM 4 -6: CPCTC 10

YOUR TURN Statements Reasons Given Vertical Angle Thrm Def’n of Midpoint SAS CPCTC 12/28/2021

YOUR TURN Statements Reasons Given Vertical Angle Thrm Def’n of Midpoint SAS CPCTC 12/28/2021 3: 16 PM 4 -6: CPCTC 11

EXAMPLE 6 Statements Reasons Given Reflexive Property 3) DEG and DEF are right angles

EXAMPLE 6 Statements Reasons Given Reflexive Property 3) DEG and DEF are right angles Given Def’n of Right Angles ASA Congruence CPCTC 12/28/2021 3: 16 PM 4 -6: CPCTC 12

YOUR TURN Statements Reasons Given AIA Given Def’n of Midpoint Vertical Angle Theorem ASA

YOUR TURN Statements Reasons Given AIA Given Def’n of Midpoint Vertical Angle Theorem ASA or AAS CPCTC 12/28/2021 3: 16 PM 4 -6: CPCTC 13

ASSIGNMENT Worksheet CPCTC 12/28/2021 3: 16 PM 4 -6: CPCTC 14

ASSIGNMENT Worksheet CPCTC 12/28/2021 3: 16 PM 4 -6: CPCTC 14