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4.1 Detours & Midpoints

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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

B D Prove: ABE ADE

Do we have enough info?

We only have sides AB AD & AE AE

We need an angle.

C

EX.1 cont.

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

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.

- 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.

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

(

)

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

1 + 6, 4 + 2 2 2

(7/2, 6/2)

(3.5, 3)