Transcript Document

Unit Five: Geometry
Lesson Three: Construct Geometric Shapes
7th Grade CCCPS
February 2013
Constructing Triangles
 One way to construct triangles is to use computer
technology. Another way is to draw it by hand using
a ruler, protractor, or both.
 If you draw it by hand you will be given certain
conditions.You can determine if it is possible to
draw one unique triangle, more than one triangle
(ambiguously defined), or no triangle at all.
Constructing Triangles
 To determine if triangles are possible, use your two
theorems:
 Triangle inequality theorem: the sum of the
lengths of any two sides of a triangle must be greater
than the length of the third side.
 You can only use this theorem if you are given side
lengths.
 Triangle angle sum theorem: the sum of the angles
in ANY triangle is 180°
 You can only use this theorem if you are given angle
measures
Is it possible?
 Not possible: If it doesn’t pass either of the two theorems
 Unique: if you are given three side lengths and they pass the
theorem, this triangle can only be drawn once. (If you change
the side lengths, its not the same triangle!)
 Ambiguously defined: if you are given three angle
measures and they pass the theorem, this triangle can be
drawn an infinite number of times, just with different side
lengths (similar triangles)
Example
A
B
F
G
E
54˚
C
Note: These two triangles have the same angle
measures and pass the angle sum theorem, but are
different sizes.
So, given these angle measures, you can draw an infinite
number of triangles that are SIMILAR!
Unique Right triangles
 Remember: a right triangle must have one right angle.
 The side lengths of a right triangle have a special relationship
based on the Pythagorean theorem (more about this in 8th
grade).
 For a triangle to be a right triangle, its side lengths will be in
triples. There are multiple triples, but the common ones are
listed below
 3,4,5 (Or any multiple of these numbers)
 5, 12, 13 (Or any multiple of these numbers)
Examples
Describe the following triangles as ambiguously defined, nonexistent, a
unique acute triangle, a unique right triangle, or a unique obtuse triangle
1.
A triangle with angles measuring 35°, 85°, and 60°?
2.
A triangle with side lengths of 2inches, 2 inches, and 1 inch
3.
A triangle with side lengths of 6cm, 8cm, and 10cm
4.
A triangle with angles measuring 45°, 90°, and 50°
Examples
1.
If Mr. Jordan wants to construct a triangle with angles
measuring 67° and 42°, what would have to be the measure of
the third angle in his construction?
2.
If Mrs. Lashley constructs a triangle with angles 44°, 23°, and
113°. If she tries to construct a different triangle with those
angle measures, what will she discover?
3.
Mrs. Radcliff constructs a triangle with one side 6cm and
another side 9cm long. Which is not a possible length for her
third side?
a. 10cm
b. 2cm
c. 7cm
d. 8cm