Discovering Geometry an Investigative Approach

Michael Serra

Chapter 2

Reasoning in Geometry - all with Video Answers

Educators

+ 2 more educators

Section 1

Inductive Reasoning

Problem 1

On his way to the local Hunting and Gathering Convention, caveperson Stony Grok picks up a rock, drops it into a lake, and notices that it sinks. He picks up a second rock, drops it into the lake, and notices that it also sinks. He does this five more times. Each time, the rock sinks straight to the bottom of the lake. Stony conjectures: “Ura nok seblu,” which translates to _________ What counterexample would Stony Grok need to find to disprove, or at least to refine, his conjecture?

Jay Patel

Jay Patel

Numerade Educator

Problem 2

Sean draws these geometric figures on paper. His sister Courtney measures each angle with a protractor. They add the measures of each pair of angles to form a conjecture. Write their conjecture.

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 3

use inductive reasoning to find the next two terms in each sequence.
1,10,100,100

Anas Venkitta

Numerade Educator

Problem 4

use inductive reasoning to find the next two terms in each sequence.
\frac{1}{6}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}

Anas Venkitta

Numerade Educator

Problem 5

use inductive reasoning to find the next two terms in each sequence.
7,3,-1,-5,-9,-13

Anas Venkitta

Numerade Educator

Problem 6

use inductive reasoning to find the next two terms in each sequence.
1,3,6,10,15,21

Anas Venkitta

Numerade Educator

Problem 7

use inductive reasoning to find the next two terms in each sequence.
1,1,2,3,5,8,12

Anas Venkitta

Numerade Educator

Problem 8

use inductive reasoning to find the next two terms in each sequence.
1,4,9,16,25,36

Anas Venkitta

Numerade Educator

Problem 9

use inductive reasoning to find the next two terms in each sequence.
32,30,26,20,12,

Anas Venkitta

Numerade Educator

Problem 10

use inductive reasoning to find the next two terms in each sequence.
1,2,4,8,16,32

Anas Venkitta

Numerade Educator

Problem 11

use inductive reasoning to draw the next shape in each picture pattern.
(shape can't copy)

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 12

use inductive reasoning to draw the next shape in each picture pattern.
(shape can't copy)

Erika Bustos

Numerade Educator

Problem 13

use inductive reasoning to draw the next shape in each picture pattern.
(shape can't copy)

Erika Bustos

Numerade Educator

Problem 14

use inductive reasoning to draw the next shape in each picture pattern.
(shape can't copy)

Erika Bustos

Numerade Educator

Problem 15

use inductive reasoning to draw the next shape in each picture pattern.
(shape can't copy)

Erika Bustos

Numerade Educator

Problem 16

use inductive reasoning to draw the next shape in each picture pattern.
(shape can't copy)

Anas Venkitta

Numerade Educator

Problem 17

Use the rule provided to generate the first five terms of the sequence

Anas Venkitta

Numerade Educator

Problem 18

Use the rule provided to generate the first five terms of the sequence
1,3,6,10, \dots, \frac{m(n+1)}{2}

Anas Venkitta

Numerade Educator

Problem 19

Now it’s your turn. Generate the first five terms of a sequence. Give the sequence to a member of your family or to a friend and ask him or her to find the next two terms in the sequence. Can he or she find your pattern?

Jay Patel

Numerade Educator

Problem 20

Write the first five terms of two different sequences in which 12 is the 3rd term.

Anas Venkitta

Numerade Educator

Problem 21

Think of a situation in which you have used inductive reasoning. Write a paragraph describing what happened and explaining why you think you used inductive reasoning.

Erika Bustos

Numerade Educator

Problem 22

The sequence $2,6,12,20,30,42, \ldots$ is called a rectangular number pattern because the terms can be visualized as rectangular arrangements of dots. What would be the 7th term in this sequence? What would be the 10 th term? The 25th term?

Anas Venkitta

Numerade Educator

Problem 23

Look at the pattern in these pairs of equations. Decide if the conjecture is true. If it is not true, find a counterexample.
$$\begin{array}{rll}
12^{2}=144 & \text { and } & 21^{2}=441 \\
13^{2}=169 & \text { and } & 31^{2}=961 \\
103^{2}=10609 & \text { and } & 301^{2}=90601 \\
112^{2}=12544 & \text { and } & 211^{2}=44521
\end{array}$$
Conjecture: If two numbers have the same digits in reverse order, then the squares of those numbers will have identical digits, but in reverse order.

Anas Venkitta

Numerade Educator

Problem 24

Study the pattern and make a conjecture by completing the fifth line. What would be the conjecture for the sixth line? What about for the tenth line?
$$\begin{array}{rcc} 1 \cdot 1 & = & 1 \\ 11 \cdot 11 & = & 121 \\ 111 \cdot 111 & = & 12,321 \\ 1,111 \cdot 1,111 & = & 1,234,321 \\ 11,111 \cdot 11,111 & = & \underline{?} \end{array}$$

Erika Bustos

Numerade Educator

Problem 25

sketch the section formed when the cone is sliced by the plane, as shown. (cone can't copy)

Anas Venkitta

Numerade Educator

Problem 26

sketch the section formed when the cone is sliced by the plane, as shown. (cone can't copy)

Anas Venkitta

Numerade Educator

Problem 27

sketch the section formed when the cone is sliced by the plane, as shown. (cone can't copy)

Anas Venkitta

Numerade Educator

Problem 28

Sketch the three-dimensional figure formed by folding the net below into a solid.

Erika Bustos

Numerade Educator

Problem 29

Sketch the figure shown below, but with the red edge vertical and facing you.

Erika Bustos

Numerade Educator

Problem 30

Sketch the solid of revolution formed when the two-dimensional figure is rotated about the line.

Erika Bustos

Numerade Educator

Problem 31

write the word that makes the statement true.
Points are $\underline{?}$ if they lie on the same line.

Erika Bustos

Numerade Educator

Problem 32

write the word that makes the statement true.
A triangle with two congruent sides is ____________.

Anas Venkitta

Numerade Educator

Problem 33

write the word that makes the statement true.
A polygon with 12 sides is called a(n)

Anas Venkitta

Numerade Educator

Problem 34

write the word that makes the statement true.
A trapezoid has exactly one pair of $?$ sides.

Anas Venkitta

Numerade Educator

Problem 35

write the word that makes the statement true.
The geometry tool used to measure the size of an angle in degrees is called a(n)

Anas Venkitta

Numerade Educator

Problem 36

write the word that makes the statement true.
$A(n) ?$ of a circle connects its center to a point on the circle.

Anas Venkitta

Numerade Educator

Problem 37

write the word that makes the statement true.
A segment connecting any two non-adjacent vertices in a polygon is called a(n)

Anas Venkitta

Numerade Educator

Problem 38

write the word that makes the statement true.
$\mathrm{A}(\mathrm{n}) ?$ polygon is both equiangular and equilateral.

Erika Bustos

Numerade Educator

Problem 39

write the word that makes the statement true.
If angles are complementary, then their measures add to

Anas Venkitta

Numerade Educator

Problem 40

write the word that makes the statement true.
If two lines intersect to form a right angle, then they are

Anas Venkitta

Numerade Educator

Problem 41

sketch and label the figure.
Pentagon GIANT with diagonal $\overline{A G}$ parallel to side $\overline{NT}$

Anas Venkitta

Numerade Educator

Problem 42

sketch and label the figure.
A quadrilateral that has reflectional symmetry, but not rotational symmetry

Erika Bustos

Numerade Educator

Problem 43

sketch and label the figure.
A quadrilateral that has reflectional symmetry, but not rotational symmetry

Erika Bustos

Numerade Educator

Problem 44

sketch and label the figure.
A counterexample to show that the following statement is false: The diagonals of a kite bisect the angles.

Erika Bustos

Numerade Educator

Problem 45

Use your ruler and protractor to draw a triangle with angles measuring $40^{\circ}$ and $60^{\circ}$ and a side between them with length $9 \mathrm{cm}$. Explain your method. Can you draw a second triangle using the same instructions that is not congruent to the first?

Allison Knapp

Numerade Educator