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HW: pgs. 336-337 (4-9, 12-14, 34, 35)
& pg. 343 (1-6, 9-14)
www.westex.org HS, Teacher Website
12-11-14
Warm up—Geometry H
B
In the figure to the right,
AB = BC and DE = EF = DF.
If the measure of ABC is 30°
E
and the measure of BDE is 50°,
D
what is the measure of DFA?
A
F
C
Note: Figure not drawn to scale
GOAL:
I will be able to:
1. apply inequalities in one triangle.
HW: pgs. 336-337 (4-9, 12-14, 34, 35) & pg. 343 (1-6, 9-14)
www.westex.org
HS, Teacher Website
Name _________________________
Date ________
Geometry H
5.5 & 5.6 Inequalities in One & Two Triangle
GOAL:
I will be able to:
1. apply inequalities in one triangle.
The positions of the ______________ and _______________ sides of a triangle are
related to the positions of the largest and smallest angles.
Example 1: Ordering Triangle Side Lengths and Angle Measures
a. Write the angles in order
b. Write the sides in order from
from smallest to largest.
shortest to longest.
YOU TRY:
a. Write the angles in order
From smallest to largest.
b. Write the sides in order from
Shortest to longest.
A triangle is formed by three segments, but not __________ set of three segments can form
a triangle.
A certain relationship must exist among the lengths of three segments in order for them to
form a triangle.
http://www.mathopenref.com/triangleinequality.html
Example 2: Applying the Triangle Inequality Theorem
Tell whether a triangle can have sides with the given lengths. Explain.
a. 7, 10, 19
b. 2.3, 3.1, 4.6
c. n + 6, n2 – 1, 3n, when n = 4.
YOU TRY:
a. 8, 13, 21
b. 6.2, 7, 9
c. t – 2, 4t, t2 + 1, when t = 4
Example 3: Finding Side Lengths
The lengths of two sides of a triangle are 8 inches and 13 inches. Find the range of
possible lengths for the third side.
YOU TRY:
The lengths of two sides of a triangle are 22 inches and 17 inches. Find the range of
possible lengths for the third side.
Example 1: Using the Hinge Theorem and Its Converse
a. Compare mBAC and mDAC.
b. Compare EF and FG.
c. Find the range of values for k.
YOU TRY:
a. Compare mEGH and mEGF.
b. Compare BC and AB.
5.5 Practice
1. Write the angles in order
from smallest to largest.
2. Write the sides in order
from shortest to longest.
3. The lengths of two sides of a triangle are 17 cm and 12 cm. Find the range of
possible lengths for the third side.
4. Tell whether a triangle can have sides with lengths 2.7, 3.5, and 9.8. Explain.
5. Ray wants to place a chair so it is 10 ft from his television set. Can the other two
distances shown be 8 ft and 6 ft? Explain.
5.6 Practice
1. Compare mABC and mDEF.
3. Find the range of values for z.
2. Compare PS and QR.