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Transcript 
5-6
5-6 Inequalities
InequalitiesininTwo
TwoTriangles
Triangles
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
GeometryGeometry
Holt
5-6 Inequalities in Two Triangles
Warm Up
1. Write the angles in order from smallest to
largest.
X,
Z,
Y
2. The lengths of two sides of a triangle are 12 cm
and 9 cm. Find the range of possible lengths
for the third side. 3 cm < s < 21 cm
Holt McDougal Geometry
5-6 Inequalities in Two Triangles
Objective
Apply inequalities in two triangles.
Holt McDougal Geometry
5-6 Inequalities in Two Triangles
Holt McDougal Geometry
5-6 Inequalities in Two Triangles
Example 1A: Using the Hinge Theorem and Its
Converse
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.
Holt McDougal Geometry
5-6 Inequalities in Two Triangles
Example 1B: Using the Hinge Theorem and Its
Converse
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.
Holt McDougal Geometry
5-6 Inequalities in Two Triangles
Check It Out! Example 1a
Compare m EGH and m EGF.
Compare the side lengths in ∆EGH
and ∆EGF.
FG = HG
EG = EG
EF > EH
By the Converse of the Hinge Theorem,
m EGH < m EGF.
Holt McDougal Geometry
5-6 Inequalities in Two Triangles
Check It Out! Example 1b
Compare BC and AB.
Compare the side lengths in ∆ABD
and ∆CBD.
AD = DC
BD = BD
m ADB > m BDC.
By the Hinge Theorem, BC > AB.
Holt McDougal Geometry
5-6 Inequalities in Two Triangles
Lesson Quiz: Part I
1. Compare m ABC and m DEF.
m ABC > m DEF
2. Compare PS and QR.
PS < QR
Holt McDougal Geometry
5-6 Inequalities in Two Triangles
Lesson Quiz: Part II
3. Find the range of values for z.
–3 < z < 7
Holt McDougal Geometry
5-6 Inequalities in Two Triangles
Lesson Quiz: Part III
4. Write a two-column proof.
Prove: m XYW < m ZWY
Given:
Proof:
Statements
Reasons
1. Given
2. Reflex. Prop. of
3. m XYW < m ZWY
Holt McDougal Geometry
3. Conv. of Hinge Thm.
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