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© Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. 1

All-In-One Answers Version BGeometryL1

Geometry: All-In-One Answers Version B

GeometryLesson 1-1 Daily Notetaking GuideL1

2 © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.

Vocabulary.

Inductive reasoning is

A is a conclusion you reach using inductive reasoning.

A counterexample is

Example.

Finding and Using a PatternFindapatternforthesequence. Use the pattern to find the next two terms in the sequence.

384,192,96,48,...

Each term is the preceding term.The next two

terms are 48 and 24 .

Quick Check.

1.Find the next two terms in each sequence.

a.1,2,4,7,11,16,22, , ,... b.Monday,Tuesday,Wednesday, ,,... c.

Answers may vary. Sample:

384 192 96 48

1 Name_____________________________________ Class____________________________ Date________________

Lesson Objective

Use inductive reasoning to make

conjectures 1

NAEP 2005 Strand:Geometry

Topic:Mathematical Reasoning

Local Standards: ____________________________________

Lesson 1-1Patterns and Inductive Reasoning

reasoning based on patterns you observe. conjecture an example for which the conjecture is incorrect. half 224
122
22
2

Thursday

2937

Friday

GeometryLesson 1-2 Daily Notetaking GuideL1

4 Name_____________________________________ Class____________________________ Date________________ © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.

Vocabulary.

An isometric drawing of a three-dimensional object shows An is the top view,front view,and right-side view of a three- dimensional figure.

A net is

Example.

Orthographic DrawingMake an orthographic drawing of the isometric drawing at right. Orthographic drawings "atten the depth of a “gure.An orthographic drawing shows views.Because no edge of the isometric drawing is hidden in the top,front, and right views,all lines are solid.

Quick Check.

1.Make an orthographic drawing from this isometric drawing.

Front Top Right

Right Front

Front Top Right

1

Lesson Objectives

Make isometric and orthographic

drawings

Draw nets for three-dimensional

figures 2 1

NAEP 2005 Strand:Geometry

Topic:Dimension and Shape

Local Standards: ____________________________________

Lesson 1-2Drawings, Nets, and Other Models

a corner view of the Þgure drawn orthographic drawing a two-dimensional pattern you can fold to form a three-dimensional figure.on isometric dot paper. three Right Front

3Daily Notetaking GuideGeometryLesson 1-1L1

© Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Name_____________________________________ Class____________________________ Date ________________

Example.

Using Inductive ReasoningMake a conjecture about the sum of the cubes of the “rst 25 counting numbers. Find the “rst few sums.Notice that each sum is a perfect square and that the perfect squares form a pattern. The sum of the “rst two cubes equals the square of the sum of the “rst counting numbers.The sum of the “rst three cubes equals the square of the sum of the “rst counting numbers.This pattern continues for the fourth and “fth rows.So a conjecture might be that

Quick Check.

2.Make a conjecture about the sum of the “rst 35 odd numbers.Use your

calculator to verify your conjecture. 133
11 1 1 1 3 1 3 2 3 1 3 2 3 3 3 1 3 2 3 3 3 4 3 1 3 2 3 3 3 4 3 5 3

225 15

2 100
10 2 36
6 2 9 3 2 1 1 2 1 2 (1 2) 2 (1 2 3) 2 (1 2 3 4) 2 (1 2 3 4 5) 2 2 Name_____________________________________ Class____________________________ Date ________________ three the sum of the cubes of the Þrst 25 counting numbers equals the square of the sum of the Þrst 25 counting numbers, or (1 2 3 . . . 25) 2 . two 1 2 2 2 3 2 4 2 5 2 1 4 9 16 25

The sum of the Þrst 35 odd numbers is 35

2 , or 1225.9 7533
575
5

Daily Notetaking GuideGeometryLesson 1-2L1

Name_____________________________________ Class____________________________ Date ________________

Example.

Drawing a NetDraw a net for the “gure with a square base and four isosceles triangle faces.Label the net with its dimensions. Think of the sides of the square base as hinges,and unfoldŽthe “gure at these edges to form a net.The base of each of the four isosceles triangle faces is a side of the .Write in the known dimensions.

Quick Check.

2.The drawing shows one possible net for the Graham Crackers box.

Draw a different net for this box.Show the dimensions in your diagram. GRAHAM

CRACKERS

GRAHAM

CRACKERS14 cm14 cm

7 cm 20 cm 20 cm 7 cm 10 cm 8 cm 2 © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. square

10 cm8 cm

Answers may vary. Example:

14 cm 7 cm 20 cmquotesdbs_dbs11.pdfusesText_17

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