The Triangle Inequality Thm.The Triangle Inequality Thm.&&

Inequalities Involving 2 TrianglesInequalities Involving 2 Triangles

Section 5-4 and 5-5

Triangle Inequality Thm.Triangle Inequality Thm.

The sum of the lengths of any two sides of a triangle is greater than the length of the 3rd side.

A

B

C

6 7

10

AB + BC > AC

Theorem 5-12Theorem 5-12

The perpendicular segment from a point to a line is the shortest segment from the point to the line.

.A

BX

Y

Corollary 5-1Corollary 5-1

The perpendicular segment from a point to a plane is the shortest segment from the point to the plane. .

SAS Inequality (Hinge Thm.)SAS Inequality (Hinge Thm.)

If 2 sides of one triangle are congruent to 2 sides of another triangle, and the included angle in one triangle is greater than the included angle in the other, then the 3rd side of the first triangle is longer than the 3rd side in the 2nd triangle.

90

100

A

B

C

D

E

F

DF > AC

SSS InequalitySSS Inequality If 2 sides of one triangle are congruent to

2 sides of another triangle and the 3rd 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 2nd triangle.

10

12

A

B

C

D

E

F

Angle E > Angle B

Joke TimeJoke Time

What would you say if someone took your playing cards?

dec-a-gon

What kind of insect is good at math?

an account-ant