Relationships in Geometry Assignment
MPM 1D
Name: _______________________
Due Date: ____________________
Part A: Knowledge and Understanding.
Determine the measures indicated. Be sure to show all your work.
1.
2.
3.
4.
5.
6.
8.
9.
7.
10.
11. Calculate the length of line segment XY.
12.
13. Which line segments in this diagram are parallel?
14. Calculate the lengths of BE, CE, AC, and BD.
15. Calculate the lengths of PT and ST given that PR measures 14 m and QS measures 10m.
16. Find the sum of the interior angles of a polygon with 10 sides.
17. Find the measure of each interior angle of a regular polygon with 7 sides.
18. How many sides does a polygon have if the sum of its interior angles is 3060°?
Part B: Communication
12. Can a triangle have two obtuse angles? Explain.
13. Can a quadrilateral have three obtuse interior angles? Explain.
14. Shauna calculates that x represents an angle measure of 50°. Is she correct? How do you
know?
Part D: Thinking
Consider the following diagram
13. Consider the following deck board problem. Show ALL your work!
Part E: Application
17. A decagon is a 10 sided polygon. The sum of the measures of nine angles of a decagon is
1400°. What is the measure of the tenth angle?
18. 3. Derek is building a deck for his summer job in the shape of a regular octagon.
a) Define: regular octagon
?
b) Determine the measure of the interior angles of the deck.
Show your work.
19. On a baseball diamond, home plate has the shape of a pentagon. The pentagon has 3 right
angles. The other 2 angles are equal.
a) What is the sum of the angles of the pentagon?
b) What is the measure of each equal angle? How do you know?
20. A Canadian $1 coin, known as a loonie, is a regular polygon with 11 sides, called an
undecagon.
a) Define a regular polygon with 11 sides.
b) Determine the sum of the interior angles of the loonie.
c) What is the size of one of the interior angles?
Now Connect Algebra to Geometry:
1. a) The sum of the interior angles in
a triangle is:
b) An equation that models the sum
of the interior angles in this
triangle is:
c) Solve the equation to determine the value of x.
d) Use the value of x to calculate the size of:
W:
Y:
Z:
2. a) The sum of the angles in a right angle is:
b) Write 2 equations to model the sums of
the 2 sets of angles that add to 90º:
(i)
(ii)
c) Solve these equations to determine the values.
(i) solve for xº
(ii) solve for yº
d) Use the values of x and y to calculate the size of:
CBP:
ABQ:
3. Write an equation and solve for the unknown. State the theorem used to make the equation.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
i°
j°
2i°
75°
k)
l)
2k°
2l° + 20°
k°
2l°
l°
m)
n)
2n°
30°
80°
2k°
120°
3n°