Download Unit 5 Constructing Shapes

Constructing Shapes
Let’s investigate whether shapes can be made with given conditions. See if
you can construct the following, and explain your findings.
Conditions
(Rules to follow
in constructing
your shapes)
Your Drawing
(Draw more than one
if possible)
Answer only ONE of these:
Yes, this is possible!
Here’s my explanation:
No, this is not possible!
Here’s my explanation:
Quadrilaterals
1) Draw a quadrilateral with 1 set of
parallel sides and
NO right angles.
2) Draw a
quadrilateral with
4 congruent
angles.
Triangles
3) Draw a triangle
with 3 equal
sides.
4) Draw a triangle
with 2 right
angles.
5) Draw a triangle
with side lengths
of 1 inch, ½ inch,
and ¼ inch.
6) Draw a triangle
with side lengths
of 3 cm, 2 cm,
and 2 cm.
7) Draw a triangle
with two obtuse
angles.
8) Draw an
isosceles triangle
with two 80⁰
angles.
Reflection: On the left page of your MSG, write a paragraph about your findings about triangles above. When
given certain conditions, are you ALWAYS able to create a triangle? What do you know MUST be true about
ANY triangle? What do you think may make it IMPOSSIBLE to make a triangle? Refer to your work above.
Constructing Shapes
Let’s investigate whether shapes can be made with given conditions. See if
you can construct the following, and explain your findings.
Conditions
(Rules to follow
in constructing
your shapes)
Your Drawing
(Draw more than one
if possible)
Answer only ONE of these:
Yes, this is possible!
Here’s my explanation:
No, this is not possible!
Here’s my explanation:
Quadrilaterals
1) Draw a quadrilateral with 1 set of
parallel sides and
NO right angles.
2) Draw a
quadrilateral with
4 congruent
angles.
Triangles
3) Draw a triangle
with 3 equal
sides.
4) Draw a triangle
with 2 right
angles.
5) Draw a triangle
with side lengths
of 1 inch, ½ inch,
and ¼ inch.
6) Draw a triangle
with side lengths
of 3 cm, 2 cm,
and 2 cm.
7) Draw a triangle
with two obtuse
angles.
8) Draw an
isosceles triangle
with two 80⁰
angles.
Reflection: On the left page of your MSG, write a paragraph about your findings about triangles above. When
given certain conditions, are you ALWAYS able to create a triangle? What do you know MUST be true about
ANY triangle? What do you think may make it IMPOSSIBLE to make a triangle? Refer to your work above.
Investigating Triangles
When given certain conditions for a triangle, sometimes you can make…
a UNIQUE triangle
(there’s only ONE triangle you can
make with those conditions)
MULTIPLE triangles
(there’s more than one way to make
a triangle with those conditions)
or NO triangle
(there’s no possible way to make
a triangle from those conditions)
Types of Triangles:
Equilateral Triangle 
(all sides are congruent,
all angles are 60⁰)
 Scalene Triangle
(no congruent sides
or angles)
Isosceles Triangle
(2 congruent sides, 2 congruent angles)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Types of Angles:
Answer the following questions based on the given conditions. You may also look back at your findings from
the previous page. Each answer should include a drawing AND a detailed explanation.
1) Conditions: A triangle with 2 obtuse angles
Will these conditions make a unique triangle, multiple triangles, or no triangle?
2) Conditions: A triangle with 3 60⁰ angles
Will these conditions make a unique triangle, multiple triangles, or no triangle?
3) Conditions: A triangle with 3 acute angles
Will these conditions make a unique triangle, multiple triangles, or no triangle?
Investigating Triangles
When given certain conditions for a triangle, sometimes you can make…
a UNIQUE triangle
(there’s only ONE triangle you can
make with those conditions)
MULTIPLE triangles
(there’s more than one way to make
a triangle with those conditions)
or NO triangle
(there’s no possible way to make
a triangle from those conditions)
Types of Triangles:
Equilateral Triangle 
(all sides are congruent,
all angles are 60⁰)
 Scalene Triangle
(no congruent sides
or angles)
Isosceles Triangle
(2 congruent sides, 2 congruent angles)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Types of Angles:
Answer the following questions based on the given conditions. You may also look back at your findings from
the previous page. Each answer should include a drawing AND a detailed explanation.
1) Conditions: A triangle with 2 obtuse angles
Will these conditions make a unique triangle, multiple triangles, or no triangle?
2) Conditions: A triangle with 3 60⁰ angles
Will these conditions make a unique triangle, multiple triangles, or no triangle?
3) Conditions: A triangle with 3 acute angles
Will these conditions make a unique triangle, multiple triangles, or no triangle?
Investigating Triangles, Continued
4) Conditions: A right triangle with an obtuse angle
Will these conditions make a unique triangle, multiple triangles, or no triangle?
5) Conditions: A right triangle with one side that is 3 inches long and one leg that is 4 inches long
Will these conditions make a unique triangle, multiple triangles, or no triangle?
Take a Closer Look:
6) Based on your findings, you know that all 3 angles on ANY triangle must add up to _________________.
7) Try drawing triangles with the side lengths listed below, and then answer the questions that follow.
a. 3 cm, 3 cm, and 3 cm
b. 12 cm, 4 cm, and 6 cm
c. 2 cm, 7 cm, and 6 cm
Were you able to draw ALL of the triangles listed above? Yes No
Are any of these triangles unique? Yes No
Which one(s)? ________________
Are any of these triangles impossible? Yes No
Which one(s)? ________________
What conditions must be given in order to create a triangle? Explain your answer clearly.
Investigating Triangles, Continued
4) Conditions: A right triangle with an obtuse angle
Will these conditions make a unique triangle, multiple triangles, or no triangle?
5) Conditions: A right triangle with one side that is 3 inches long and one leg that is 4 inches long
Will these conditions make a unique triangle, multiple triangles, or no triangle?