Download Shapes and Designs

Shapes and Designs
Name: ______________________________ Per: _____
Unit Standards
7.G.2: Draw, with ruler and protractor, triangles with given conditions.
7.G.2: Identify when the conditions determine a unique triangle, more than one triangle or no triangle.
7.G.5: Use facts about supplementary, complementary, vertical, and adjacent angles to write and solve simple
equations for an unknown angle in a figure.
Problem 2.2: Interior Angle Sum of a Triangle, Problem 2.4: Finding Missing Angles in Triangles
Measure the interior angles in each triangle and find the sum.
Triangle
Angle 1
1
2
3
4
What is the sum of the interior angles in any triangle?
Angle 2
Angle 3
Write and Solve An Equation
to Find the Sum of the Angles
∠1 +∠2+∠3 = ____
If you know the sum of the interior angles of a triangle is always __________, then you can solve for a missing
angle in a triangle.
A. For each of the triangles below, write and solve an equation to find the value of the unknown angle.
Use the results to find the size of each angle.
B. For each of the triangles below, write and solve an equation to find the value of x and then find the
size of each angle.
Continue to next page…
Challenge: 
Homework:
Find the missing angle in each of the triangles below. Make sure that you write an equation for each problem.
Example:
Equation: 65 + 45 + x = 180
180 – 110 = 70
Equation: _________________
Equation: ________________
Angle: ∠FDE = 70⁰
Angle: ____________________
Angle: ____________________
Equation: _________________
Equation: _________________
Equation: ________________
Angle: ____________________
Angle: ____________________
Angle: ____________________
Continue to next page…
Find the missing angle in each of the triangles below. Make sure that you write an equation for each problem.
Equation: _________________
Equation: _________________
Equation: ________________
Angle: ____________________
Angle: ____________________
Angle: ____________________
Find the missing angle in each of the angle relationships below. Make sure that you write an equation for each
problem.
10.
11.
12.
These two angles are (Circle one):
Complementary/Supplementary
These two angles are (Circle one):
Complementary/Supplementary
These two angles are (Circle one):
Complementary/Supplementary
Equation: _______________
Equation: _______________
Equation: _______________
Angle x= _________
Angle x= _________
Angle x= _________
13.
14.
15.
These two angles are (Circle one):
Complementary/Supplementary
These two angles are (Circle one):
Complementary/Supplementary
These two angles are (Circle one):
Complementary/Supplementary
Equation: _______________
Equation: _______________
Equation: _______________
Angle x= _________
Angle x= _________
Angle x= _________
Problem 3.1: Building Triangles
A. Try to make a triangle from the given side lengths. If you can build a triangle, make a sketch.
Side Lengths
Triangle
Possible?
Sketch Triangle
1. List some side lengths that did make a
triangle.
3, 4, 5
1, 1, 3
2, 4, 7
2. List some side lengths that did NOT
make a triangle.
2, 3, 4
4, 5, 7
2, 3, 8
B. Look at your table.
1. What pattern do you see to explain why some sets of numbers make a triangle and some do not?
2. For what side length relationships can you make more than one triangle from a given set of side
lengths?
3. Find three other side lengths that make a triangle. Then find three other side lengths that will NOT
make a triangle.
Homework:
Problem 3.2: Design Challenge II
Use the directions provided to draw a triangle congruent to the one below.
Triangle ABC
#1
#2
#3
These directions may seem like they would also produce a triangle that is congruent, but they do not. Construct
a triangle that meets the criteria but is not congruent to triangle ABC.
#4
#5
What minimum information about a triangle allows you to draw exactly one triangle?
You need to have at least ________________ sides and/or angle measurements – but not any
______________.
You can make a unique triangle with ________________ side lengths or with ________ angles and
_________ side length.
Homework:
1. Multiple Choice:
Explain your reasoning:
2. Construct these triangles based on the criteria (use a ruler and protractor):
An equilateral triangle with sides of 1.5 inches. (Hint: A right triangle with legs of 1.5 inches and 1.75
Think about the angles in an equilateral triangle.)
inches.
A triangle with a 25 degree angle and legs of 2.25
inches and 3.75 inches.
A triangle with a 70 degree angle with sides of 1.5
inches and 2.25 inches.
Problem 3.4: Vertical Angles
A. Use the diagram at right as you work through
problems 1-4:
1. Suppose angle b and angle f are 80 degrees.
Find the rest of the angles in the diagram
(label them on the diagram).
You probably noticed that when two lines
intersect four angles are formed. The opposite
pairs of angles are called vertical angles. For
example, in the diagram angles f and g are
vertical angles.
2. Name the three other pairs of vertical
angles in the diagram:
3. Name the eight pairs of supplementary angles in the diagram:
4. What is true about the measures of any vertical angle pair? Explain how you know.
Use what you know about complementary, supplementary,
and vertical angles. Write an equation then find the value of
x and the size of each angle in this figure.
Equation to Solve for x:
x = ______
∠BAE: ______
∠EAF: ______
∠FAD: ______
∠DAC: ______
∠CAB: ______
Last Step: Check your work! What do all of your angles add up to? If they add up to full rotation (360°), you
are on the right track!
Homework:
Problem 3.4: Practice with All Angle Relationships
Angle Relationships:
Complementary angles add up to ______.
The complement of 30° is _____.
30°
Supplementary angles add up to ______.
The supplement of 30° is _____.
Vertical angles are __________________.
The vertical angle to 30° is _____.
Write an equation and show how to find each missing angle with a number. Identify which angle relationship
you used to solve the problem. See the example:
Example:
Equation:
∠1 + 57° = 180°
180° – 57° = 123°
Relationship:
Supplementary angles
m∠1 = 65°
Equation:
Equation:
Relationship:
Relationship:
m∠2 = 67°
Equation:
Equation:
Equation:
Relationship:
Relationship:
Relationship:
Continue to the next page…
Ok, now it’s going to get trickier… You need to solve for x and then find both angles. See the example:
Example:
Equation:
Equation:
4x + 11 + 3x + 1 = 180°
7x + 12 = 180°
7x = 168°
x = 24
Angles:
Angles:
∠13 = 4x + 11 = 4(24) + 11
∠14 = 3x + 1 = 3(24) + 11
Check:
What is the angle relationship?
Check:
What is the angle relationship?
Does my answer seem reasonable? Yes/No
Does my answer seem reasonable? Yes/No
Now, find the three missing angles in this problem! You’re almost done!
Equation:
Angles: