4 1 detours midpoints
This presentation is the property of its rightful owner.
Sponsored Links
1 / 7

4.1 Detours & Midpoints PowerPoint PPT Presentation


  • 86 Views
  • Uploaded on
  • Presentation posted in: General

4.1 Detours & Midpoints. Obj: Use detours in proofs Apply the midpoint formulas. Detour Proofs: used when you need to prove 2 pairs of s  to solve a case. Ex:1 A E Given: AB  AD BC  CD

Download Presentation

4.1 Detours & Midpoints

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


4 1 detours midpoints

4.1 Detours & Midpoints

Obj: Use detours in proofs

Apply the midpoint formulas


Detour proofs used when you need to prove 2 pairs of s to solve a case

Detour Proofs: used when you need to prove 2 pairs of s  to solve a case.

Ex:1

A E Given: AB  AD

BC  CD

B D Prove: ABE ADE

Do we have enough info?

We only have sides AB  AD & AE  AE

We need an angle.

C


Prove abc adc first by sss

EX.1 cont.

Prove ABC  ADC First by SSS

Reasons

Given

Given

Reflexive Property

SSS (1,2,3)

CPCTC

Reflexive Property

SAS (1,5,6)

Statements

  • (S) AB  AD

  • (S) BC  DC

  • (S) AC  AC

  • ABC  ADC

  • (A)  BAC DAC

  • (S) AE  AE

  • ABE  ADE


Procedure for detour proofs

Procedure for Detour Proofs

Determine which triangles you must prove to be congruent to reach the required conclusion.

Attempt to prove that these triangles are congruent. If you cannot do so for lack of enough information, take a detour.

Identify the parts that you must prove to be congruent to establish the congruence of the triangles.


Procedure for detour proofs1

Procedure for Detour Proofs

  • Find a pair of triangles that

    • You can readily prove to be congruent.

    • Contain a pair of parts needed for the main proof.

  • Prove that the triangles found in step 4 are congruent.

  • Use CPCTC and complete the proof planned in step 1.


Midpoint formula for the midpoint of a line take the average of two given points x m x 1 x 2

Midpoint formula: for the midpoint of a line take the average of two given points. Xm = X1 + X2

2

X = -2 + 8 2

= 6 2

=3

A B

X3

-2

8

EX.2: Find the midpoint of line segment AB

equal distance, hence midpoint


Midpoint formula for segment on the coordinate plane

Midpoint formula for segment on the coordinate plane:

(

)

Find the midpoint of (1, 4) and (6, 2).

1 + 6, 4 + 2 2 2

(7/2, 6/2)

(3.5, 3)


  • Login