5-6: Inequalities Involving 2 Triangles

1
5-6 Inequalities Involving 2 Triangles

• Expectation
• G1.2.2 Construct and justify arguments and solve
  problems involving angle measure, side length,
  perimeter and area of all types of triangles.

2
In the triangles below, 2 pairs of corresponding
sides are congruent. Compare the third sides.
x
2.17
2.17
y
82
32
2.67
2.67
3
SAS Inequality (Hinge Theorem)

• If two sides of one triangle are congruent to 2
  sides of a second triangle, but the included
  angle of the first is greater than the included
  angle of the second, then the 3rd side of the
  first is _______________ than the 3rd side of the
  second.

4
Two pairs of corresponding sides are congruent in
the triangles below. Compare the included angles
for the given congruent sides.
5
SSS Inequality

• If two sides of one triangle are congruent to 2
  sides of a second triangle, but the third side of
  the first is longer than the third side of the
  second, then the included angle between the pair
  of congruent sides of the first is ______________
  than the included angle between the pair of
  congruent sides of the second.

6
Use the figure to compare the indicated measures.
E
8
D
10
10
9
6
C
8
A
B
9
a. m?ADB and m?DBC
7
Use the figure to compare the indicated measures.
E
8
D
10
10
9
6
C
8
A
B
9
b. m?EAD and m?BCD
8
In ?ABC and ?DEF below (not drawn to scale) AB,
BC, DE and EF are all 12 units long. If m?A 30
and m?F 50, compare AC and DF.

1. AC DF
2. AC gt DF
3. AC lt DF
4. not enough information given to determine an
   answer.

9
Given QC bisects PD and m?PCQ gt m?DCQ
Prove m?D gt m?P
P
C
D
Q
10
Assignment pages 277, 15 - 29 (odds)