Summer Packet

Geometry CC Regents

2016-2017

Directions: This packet is for students going into Geometry CC Regents. Answer all questions in this packet. These questions will prepare you for the subject. Your teacher in September will go over the answers in class. This packet will be graded. Do the best you can!

Perfect Squares

Fill in as many values as you can FROM memory. You do NOT need to go in order. The goal is to assess your memory, so if you don’t know a fact immediately, write a “?” —do NOT calculate!

122 = / 302 = / 182 = / 192 =
152 = / 72 = / 132 = / 252 =
202 = / 142 = / 162 = / 62 =
112 = / 212 = / 172 = / 102 =
1002= / 302 = / 242 = / 92 =

When you are done, list the facts below that you did not know by heart below. Try to learn them before school starts in September. 

In Grade 8, you studied the Pythagorean theorem.

Explain it below, and explain how knowing squares can make Pythagorean Theorem problems easier.

Solving Linear Equations

Answer the following examples of linear equations. You need to show your work. Remember your work must be your own.

1)What is the solution of the equation? Justify each step.

2)Find the solution of the equation. Justify each step.

3)A square field has an area of 479 ft. What is the approximate length of a side of the field? Give your answer to the nearest foot. Justify your answer.

4)A mountain climber ascends a mountain to its peak. The peak is 12,740 ft above sea level. The climber then descends 200 ft to meet a fellow climber. Find the climber’s elevation above sea level after meeting the other climber.

5)A camera manufacturer spends $2250 each day for overhead expenses plus $6 per camera for labor and materials. The cameras sell for $16 each.

  1. How many cameras must the company sell in one day to equal its daily costs?
  1. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?

6)What is the solution of the equation? Justify each step.

Solving Proportions

Solve the proportion below as many ways as you can think of. You need to show at least four different ways. You can ask people for inspiration (but your work must be your own!)

Example methods include:

Using factors of change across the fractions.

Using factors of change within the fractions

Cross multiplying.

Making patterns.

Multiplying both sides by the same value

Simplifying fractions first

Trial and Error

Basic Terms

Term / Description in words
(If you don’t remember, look up in a dictionary) / Example from the real world
Point
Line
Segment
Plane

Write a sentence distinguishing what acute, obtuse, and right angles. Include diagrams with your sentence.

Triangles

Make a list of every type of triangle you have ever studied. The last row is fully blank for you to add anything missing from the list.

Type / Description in words
(If you don’t remember, look up in a dictionary) / Drawing of an example
Scalene /
isosceles
All angles are less than 90°
One angle is 90°
One angle is greater than 90°

Quadrilaterals

Fill in the family tree below.

Transversals

In the diagram below, lines m and n are parallel.

Make a list of everything you see in the diagram below. There is a LOT to describe! Many angles are congruent (equal) and supplementary. Also, there are names for the lines and the angles. Here are some vocabulary terms that you can use in your list.

Parallel lines, Transversal, Vertical angles, Alternate interior angles, Corresponding angles, Alternate exterior angles , Interior angles on the same side of the transversal

Sequences of Patterns

For each example find the sequence of patterns. You need to show and justify your answer for each example. You should work on each example on your own.

1)Bobby has a set of tiles similar to the ones shown below. He says that his tiles have a total of 9 red triangles. Is 9 a reasonable number of triangles?

2)The table shows the relationship between the number of white triangles and the total number of square tiles in each figure. Complete the table and extend the pattern. What is the total number of white triangles in afigure with 6 tiles?

Number of Square Tiles (s) / Number of White Triangles (t)
1 / 4
2
3
4
5