# unit 5 review

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Unit 5 Review Sheet

Logic & Triangles

Learning Goal 1: Students will use logic and reasoning to make conjectures MM1G2 a, b

Knowledge and Understanding:

1. Your teacher writes the following sequence of numbers on the board: 3, 7, 11, and 15. He tells
you that each number in the sequence is 4 more than the number before it. You determine that
the next number in the sequence is 19. What type of reasoning did you use to reach your
conclusion? Why?

2. Which is the converse, inverse and contrapositve of the following statement?

Statement: If a quadrilateral has four congruent sides, then it is a rhombus.

Application:

3. Write the following statement as a biconditional statement?
 If a quadrilateral is a square, then it has 4 right angles.

4. Consider the following statements. What is a valid conclusion that can be reached using the
following statements? (Hint: Use the Law of Syllogism/Chain Rule)

Statement: If Takira does not have any homework this weekend, she is going camping with her
friends.
Statement: Takira has homework.

Extension:

5. What additional statement is required to reach the given conclusion? Why?

Statement: Students can get free admission to the movie if they present their student
identification card.

Statement: ?

Conclusion: Therefore, Mary did not bring her student identification card.
Learning Goal 2: Students will determine possible lengths of triangles as well as determine if two
triangles are congruent. MM1G3 b, c                                            Score:

Knowledge and Understanding                                                   D        M         E

1. The sides of a triangle are 12, 7, and x. Use the Triangle Inequality Theorem to determine the
length of the third side.

2. Use the diagram below to complete the congruence statements ∆GJH            ∆_____ by ______.

H

G               J               I
Application:                                                          G

3. In ∆CAT, m < C = 540 and m < T = 360. What is the longest side of the triangle? (Hint: Draw
a picture)

4. What information would be needed in order to prove the following two triangles congruent by
SAS?
K                                  L

N

J                              M
Extension:

5. Using the diagram below, order the sides from greatest to least.
d
40   0                           450
280

e
h                  g

280
f
Learning Goal 3: Students will understand and use points of concurrency in a triangle. MM1G3 e
Score:
Knowledge and Understanding
D        M   E
1. The medians of a triangle concur at the _____________________.

2. The Circumcenter is the point of concurrency in a triangle where the __________________
intersect.

Application:

Use the diagram below to answer questions 3 and 4, P is the centroid of ∆ABC and PD = 3.
B
3. Find BP. How do you know?

E       P                C

4. Find BD. How do you know?                                                D
A

Extension:

5. Given the diagram below with GE, GD and GF are perpendicular bisectors of the
sides of the triangle.

C
G

E
F

A       D       B

a. G is the ____________________ of the triangle.

b.     ABC is an obtuse triangle. How do you know this from the diagram
without measuring the angles?

c. If G is on ABC what kind of triangle would it be?
Unit 5 Review Sheet

Learning Goal 4: Students will determine interior and exterior angles of polygons. MM1G3 a

Knowledge and Understanding:                                                      Score:

1. Calculate the sum of the interior angles of a convex hexagon.           D         M          E

2. Determine the sum of the exterior angles of any convex polygon.

Application:

3. How many sides does a convex polygon have if the measure of its interior angles have a
sum of 28800?

3x0            4x0
4. What is the value of x in the figure to the right?

2x0                              4x0

2x0
5x0

Extension: (provide an explanation to receive full credit!!)

5. In a certain regular polygon, the measure of an interior angle is equal to the measure of an
exterior angle. How many sides does the polygon have? How do you know?

Explanation:
Learning Goal 5: Students will understand and use properties of quadrilaterals. MM1G3d.
Score:

D        M       E
Knowledge and Understanding:

1. Which quadrilateral below has exactly one pair of parallel sides?

2. Opposite angles of a parallelogram are _______________________.

Application:

3. Which statement would NOT prove that ABDC is a parallelogram?
A                                 B
a.
b.
c.
d.                                                     C
D

4. Use the figure to the right to find LP (note: the figure is not drawn to scale).

Extension: (You must show work to receive credit!)

5. Given square MNOP. The perimeter of MNOP is 72 cm and NO = 2x + 6. Find x. (Hint:
Draw a picture)

Work:
Learning Goal 6: Students will understand and use the formulas for calculating midpoint and distance.
M1G1 a-e
Score:
Knowledge and Understanding:                                                   D        M        E
1. Calculate the distance between the points (-3, 2) and (1, -3)

2. Find the midpoint between the points (5, 12) and (13, 8)

Application:

3. Find the coordinates of the other endpoint of a segment with an endpoint of X(-2, 3) and a
midpoint M(1, -3). (Hint: Draw a picture)

4. The distance between two points is 7, and the points are (5, 2) and (x, 4). Find the value for x.
(Hint: Draw a picture)

Extension: (You must show work to receive full credit!!)

5. Two fish are stocked into a lake from a boat. The first swims 1 mile north and 2 miles east. The
second swims 3 miles west then 2 miles north. How many miles apart are the fish? (Hint: Draw
a picture)

Work:

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