Page 142 - Math Course 2 (Book 2)

Inequalities: Two Triangles
Mo. 10

Lesson 6

4. m∠JKH < m∠KHL Subtraction Property
5. JK = HL Given
KEY CONCEPTS:
6. HK = HK Reflexive Property
1. Apply the SAS Inequality.
2. Apply the SSS Inequality. 7. JH < KL SAS Inequality
3. Finding the relationships between two
triangles.
THEOREM 10.12

MO. 10 - L6a SAS Inequality / Hinge Theorem

Applying the SAS and Two sides of a triangle are congruent to two sides
SSS Inequality of another triangle. If the included angle in the first
triangle has a greater measure than the included
angle measure than the included angle in the
second triangle, then the third side of the first
triangle is longer than the third side of the second
Let’s Begin triangle.

Given AB ≅ PQ, AC ≅ PR,
Example
Use SAS Inequality in a Proof if m∠1 > m∠2, then BC > QR.
B Q
Example

Write a two-column proof.

1 2
Given: KL || JH
m∠JKH + m∠HKL < m∠JHK + m∠KHL A C P R
JK = HL

Prove: JH < KL THEOREM 10.13
K
J SSS Inequality Theorem
If two sides of a triangle are congruent to two
sides of another triangle and the third side in one
triangle is longer than the third side in the other,
then the angle between the pair of congruent
H sides in the first triangle is greater than the
L corresponding angle in the second triangle.

Proof: Given AB ≅ PQ, AC ≅ PR,
Statements Reasons Example if BC > QR, then m∠1 > m∠2

1. m∠JKH + m∠HKL < Given B Q
m∠JHK + m∠KHL

Alternate interior angles
2. m∠HKL = m∠JHK
are congruent
3. m∠JKH + m∠JHK < Substitution 1 2
m∠JHK + m∠KHL
A C P R
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