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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

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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)

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