Title: 5-4: Inequalities for Sides and Angles of a Triangle
15-4 Inequalities for Sides and Angles of a
Triangle
- Expectation
- G1.2.2 Construct and justify arguments and solve
multi-step problems involving angle measure, side
length, perimeter and area of all types of
triangles. -
2- The highest and lowest temperatures recorded in
New York one year were 38 degrees Celsius and -21
degrees Celsius. The next year the highest and
lowest temperatures were 36C and -25ºC. - What was the difference in the lowest and highest
temperatures over the two years?
3Scalene Triangles
a. Draw a scalene triangle.
b. Determine the measures of all of the sides and
all of the angles.
c. List the angles in terms of their measures
from smallest to largest.
4Scalene Triangles
d. List the sides in terms of their measures from
smallest to biggest.
e. Conjecture a relationship between the measures
of the angles and the lengths of the sides of the
triangle.
5Unequal Sides Theorem
- If one side of a triangle is longer than another,
then the angle opposite the longer side has
___________ measure than the angle opposite the
shorter side.
The larger angle is opposite the longer side.
6Unequal Angles Theorem
- If one angle of a triangle has greater measure
than another angle, then the side opposite the
larger angle is _____________ than the side
opposite the smaller angle.
The longer side is opposite the larger angle.
7Order the sides from longest to shortest.
C
37
105
A
B
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9Order the angles from largest to smallest.
Y
27
38
X
42
Z
10Triangle ABC has vertices A(0,0), B(4,7) and
C(-2,-3). List the angles in terms of size from
smallest to largest.
11List the sides of ?ABC in order from shortest to
greatest
- m?A 9x - 4, m?B 4x - 16, m?C 68 - 2x
12Distance Between a Point and a Line Theorem
- The shortest distance from a line to a point not
on the line is the length of a perpendicular
segment from the point to the line.
13Prove the Distance Between a Point and a Line
Theorem by using an indirect proof.
- Given TR ? m, R and L are distinct points
- Prove TL gt TR
T
R
L
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15Distance Between a Point and a Plane Corollary
- The shortest distance from a plane to a point not
on the plane is the length of a perpendicular
segment from the point to the plane.
16Name the longest segment in ?CED.
E
A
55
30
50
D
100
40
B
C
17Name the longest segment in the figure.
E
A
55
30
50
D
100
40
B
C
18Given AD gt CD, m?A gt m?ADB and m?ABD gt m?DBC,
which of the following statements must be true?
- AB gt BD
- m?BCD lt m?ADB
- ?A ? ?C
- m?A lt m?C
- BD gt CD
19Assignment
- pages 263-264,
- 15 26 (all), 29 and 32