Transcript Inequalities Involving Two Triangles

Inequalities Involving Two
Triangles
SAS Inequality/Hinge Theorem
• If two sides of one 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.
Write a two-column proof.
Given: m1 < m3
E is the midpoint of
Prove: AD < AB
Proof:
Statements
Reasons
1. E is the midpoint
of
1. Given
2.
3.
4.
5.
6.
7.
2. Definition of midpoint
3. Reflexive Property
4. Given
5. Definition of vertical angles
6. Substitution
7. SAS Inequality
Inequalities Involving Two
Triangles
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 an inequality using the information in the figure.
a.
Answer:
b. Find the range of values
containing n.
Answer: 6 < n < 25
Given: X is the midpoint of
MCX is isosceles.
CB > CM
Prove:
Proof:
Statements
1. X is the midpoint of
2.
3. MCX is isosceles.
4.
5.
6.
7.
Reasons
1. Given
2. Definition of midpoint
3. Given
4. Definition of isosceles
triangle
5. Given
6. Substitution
7. SSS Inequality