Transcript Slide 1

Example 1A: Compare mBAC and mDAC.
Compare the side lengths in ∆ABC
and ∆ADC.
AB = AD
AC = AC
BC > DC
By the Converse of the Hinge Theorem,
mBAC > mDAC.
Example 1B: Compare EF and FG.
Compare the sides and angles in
∆EFH angles in ∆GFH.
mGHF = 180° – 82° = 98°
EH = GH
FH = FH
mEHF > mGHF
By the Hinge Theorem, EF < GF.
Example 1C: Find the range of values for k.
Step 1 Compare the side lengths in
∆MLN and ∆PLN.
LN = LN
LM = LP
MN > PN
By the Converse of the Hinge Theorem,
mMLN > mPLN.
5k – 12 < 38
Substitute the given values.
k < 10
Step 2 Since PLN is in a triangle, mPLN > 0°.
5k – 12 > 0
Substitute the given values.
k > 2.4
Step 3 Combine the two inequalities.
The range of values for k is 2.4 < k < 10.
Example 2: Travel Application
John and Luke leave school at the same time. John
rides his bike 3 blocks west and then 4 blocks north.
Luke rides 4 blocks east and then 3 blocks at a bearing
of N 10º E. Who is farther from school? Explain.
The distances of 3 blocks
and 4 blocks are the
same in both triangles.
The angle formed by
John’s route (90º) is
smaller than the angle
formed by Luke’s route
(100º). So Luke is farther
from school than John by
the Hinge Theorem.
Example 3: Proving Triangle Relationships
Write a two-column proof.
Given:
Prove: AB > CB
Proof:
Statements
Reasons
1. Given
2. Reflex. Prop. of 
3. Hinge Thm.
Example 3B Write a two-column proof.
Given: C is the midpoint of BD.
m1 = m2
m3 > m4
Prove: AB > ED
Statements
1. C is the mdpt. of BD
m3 > m4,
m1 = m2
Reasons
1. Given
2. Def. of Midpoint
3. 1  2
3. Def. of  s
4. Conv. of Isoc. ∆ Thm.
5. AB > ED
5. Hinge Thm.