Warm-up

1
Warm-up

• 1) Write an inequality to describe the length of
  MN. (Look at the picture)

2) Find the range for the measure of the third
side of a triangle if two sides measure 4 and 13.
3) Can these 3 lengths for a triangle? a) 6,
6, 12 b) 10, 8, 6 c) 3, 2, 2
2
5-6 Inequalities in 2 Triangles
3
Hinge Theorem (You dont have to write every
word!)

• If 2 sides of a triangle are cong. to 2 sides of
  another triangle the incl. ang. of 1 triangle
  is greater than the incl. ang. of the other
  triangle,
• then the 3rd side of the 1st triangle is larger
  than the 3rd side of the 2nd triangle.

Y
B
50
60
A
C
X
Z
4
Converse Hinge Thm (you dont have to write every
word!)

• If 2 sides of a triangle are cong. to 2 sides of
  another triangle the 3rd side of 1 triangle is
  greater than the 3rd side of the other triangle,
• then the ang. inside the cong. sides of the 1st
  triangle is larger than the ang. inside the cong.
  sides of the 2nd triangle.

Y
B
15
20
A
C
X
Z
5
Example
Compare the measures AD and BD.
Answer By the Hinge Theorem, m?ACD gt m?BCD, so
AD gt DB.
6
Example
Compare the measures m?ABD and m?BDC.
Answer By the Converse of the Hinge Theorem,
m?ABD gt m?BDC.
7
TOO
A. FG gt GH B. FG lt GH C. FG GH D. not enough
information
8
TOO
Compare m?JKM and m?KML.
A. m?JKM gt m?KML B. m?JKM lt m?KML C. m?JKM
m?KML D. not enough information
9
Think-Pair-Share!
Meena and Rita are both flying kites in a field
near their houses. Both are using strings that
are 10 meters long. Meenas kite string is at an
angle of 75 with the ground. Ritas kite string
is at an angle of 65 with the ground. If they
are both standing at the same elevation, which
kite is higher in the air?
A. Meenas kite B. Ritas kite
10
HW WS 5-6 Practice