Download E - mrhubbard

Lesson 5-5 Inequalities involving two
triangles
• Theorem 5.13 SAS Inequality/Hinge Theorem
– If two sides of a triangle are congruent to two sides of
another triangle and the included angle in one triangle has
a greater measure than the included angle in the other,
then the third side of the first triangle is longer than the
third side of the second triangle.
• Theorem 5.14 SSS Inequality
– 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 sides in the first triangle is greater
than the corresponding angle in the second triangle.
Write a two-column proof.
Given:
Prove:
Proof:
Statements
Reasons
1.
1. Given
2.
2. Alternate interior angles
are congruent.
3.
3. Substitution
4.
5.
6.
7.
4. Subtraction Property
5. Given
6. Reflexive Property
7. SAS Inequality
Write a two-column proof.
Given:
m1 < m3
E is the midpoint of
Prove: AD < AB
Proof:
Statements
1.
E is the midpoint
2. of
3.
4.
5.
6.
7.
Reasons
1. Given
2. Definition of midpoint
3. Reflexive Property
4. Given
5. Definition of vertical angles
6. Substitution
7. SAS Inequality
Given:
Prove:
Proof:
Statements
Reasons
1.
2.
3.
1. Given
2. Reflexive Property
3. Given
4.
4. Given
5.
6.
5. Substitution
6. SSS Inequality
Given:
Prove:
X is the midpoint of
MCX is isosceles.
CB > CM
Proof:
Statements
1.
2. X is the midpoint of
3.
4.
MCX is isosceles.
5.
6.
7.
Reasons
1. Given
2. Definition of midpoint
3. Given
4. Definition of isosceles triangle
5. Given
6. Substitution
7. SSS Inequality
Write an inequality comparing mLDM and mMDN
using the information in the figure.
The SSS Inequality allows us to conclude that
Answer:
Write an inequality finding the range of values
containing a using the information in the figure.
By the SSS Inequality,
SSS Inequality
Substitution
Subtract 15 from each side.
Divide each side by 9.
Also, recall that the measure of any angle is always
greater than 0.
Subtract 15 from each side.
Divide each side by 9.
The two inequalities can be written as the compound
inequality
Answer:
Write an inequality using the information in the figure.
a.
b. Find the range of values
containing n.
Answer:
Answer: 6 < n < 25