• Home

  • Documents

  • JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and...
14
JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior angles of a triangle Discover properties of the base angles and the vertex angle bisector in isosceles triangles Discover inequalities among sides and angles in triangles Investigate SSS, SAS, SSA, ASA, SAA, and AAA as potential shortcuts to proving triangle congruence Show that pairs of angles or pairs of sides are congruent by identifying related triangles and proving them congruent, then applying CPCTC Create flowchart proofs Review algebraic properties and methods for solving linear equations Develop logical and visual thinking skills Develop inductive reasoning, problem solving skills, and cooperative behavior

JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

Tags:

Embed Size (px)

Citation preview

Page 1: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.2 HGSH

C H A P T E R 4 O B J E C T I V E S

Discover and explain sums of the measures of two and three interior angles of a triangle

Discover properties of the base angles and the vertex angle bisector in isosceles triangles

Discover inequalities among sides and angles in triangles

Investigate SSS, SAS, SSA, ASA, SAA, and AAA as potential shortcuts to proving triangle congruence

Show that pairs of angles or pairs of sides are congruent by identifying related triangles and proving them congruent, then applying CPCTC

Create flowchart proofs

Review algebraic properties and methods for solving linear equations

Develop logical and visual thinking skills

Develop inductive reasoning, problem solving skills, and cooperative behavior

Practice using geometry tools

Page 2: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.2 HGSH

Algebra I Review

These properties allow you to perform the same operation on both sides of an equation.

This property allows you to check your solution to an equation by replacing each variable with its value. Substitution is also used to solve some equations and in writing proofs.

Page 3: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.2 HGSH

More Examples:

Page 4: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.3 HGSH

How long must each side of this drawbridge be so that the bridge spans the river when both sides come down?

The sum of the lengths of the two parts of the drawbridge must be equal to or greater than the distance across the waterway.

Triangles have similar requirements.

Page 5: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.3 HGSH

Page 216

http://mathopenref.com/triangleinequality.html

http://mathopenref.com/triangleinequality.html
http://mathopenref.com/triangleinequality.html
Page 6: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.3 HGSH

http://mathopenref.com/trianglesideangle.html

http://mathopenref.com/trianglesideangle.html
http://mathopenref.com/trianglesideangle.html
Page 7: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.3 HGSH

So far in this chapter, you have studied interior angles of triangles. Triangles also have exterior angles. If you extend one side of a triangle beyond its vertex, then you have constructed an exterior angle at that vertex.

Each exterior angle of a triangle has an adjacent interior angle and a pair of remote interior angles. The remote interior angles are the two angles in the triangle that do not share a vertex with the exterior angle.

Page 8: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.3 HGSH

http://mathopenref.com/triangleextangletheorem.html

http://mathopenref.com/triangleextangletheorem.html
http://mathopenref.com/triangleextangletheorem.html
Page 9: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.4 HGSH

A building contractor has just assembled two massive triangular trusses to support the roof of a recreation hall. Before the crane hoists them into place, the contractor needs to verify that the two triangular trusses are identical. Must the contractor measure and compare all six parts of both triangles?

Third Angle Conjecture : If there is a pair of angles congruent in each of two triangles, then the third angles must be congruent. But will this guarantee that the trusses are the same size? You probably need to also know something about the sides in order to be sure that two triangles are congruent.

Recall from earlier exercises that fewer than three parts of one triangle can be congruent to corresponding parts of another triangle, without the triangles being congruent.

Page 221

Do all six pairs of congruencies need to be shown in order to prove that two triangles are congruent ?

Page 10: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.4 HGSH

You will investigate three of these cases in this lesson and the other three in the next lesson to discover which of these six possible cases turn out to be congruence shortcuts and which do not.

So let’s begin looking for congruence shortcuts by comparing three parts of each triangle. There are six different ways that the three corresponding parts of two triangles may be congruent. They are diagrammed below. Some of these will be congruence shortcuts, and some will not.

Page 11: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.4 HGSH

Page 222

SSS

http://www.mathopenref.com/congruentsss.html
Page 12: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.4 HGSH

SAS

http://mathopenref.com/congruentsas.html
Page 13: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.4 HGSH

SSA

http://mathopenref.com/congruentssa.html
Page 14: JRLeon Discovering Geometry Chapter 4.2 HGSH C H A P T E R 4 O B J E C T I V E S Discover and explain sums of the measures of two and three interior

JRLeon Discovering Geometry Chapter 4.2 HGSH

Classwork: Group 4.3: .pp 218 – 219 # 1, 3 and 5Group 4.4: .pp 224 – 225 # 2, 4 and 6Homework: 4.3: .pp 218 – 219 # 2-18 Even and # 174.4: .pp 224 – 225 # 1-21 Odds


JRLeon Discovering Geometry Chapter 3.3 HGSH Look over at one of the walls. What is the distance from where you are to that wall? How would you measure

JRLeon Discovering Geometry Chapter 3.3 HGSH Look over at one of the walls. What is the distance from where you are to that wall? How would you measure

Documents
RíoJat 0 N LA INDEPENDENCIA M APUN IC L 4 filee e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

RíoJat 0 N LA INDEPENDENCIA M APUN IC L 4 filee e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Documents
e INSTITUTO DE ALTOS ESTUDIOS NACIONALESrepositorio.iaen.edu.ec/bitstream/24000/4004/1/Sangoluisa...e OS-34 1 e 2007 ( ( e e e e e ( e e e e ( ( e e e e e e e e e e e e e e e e ~ROPIEDAD

e INSTITUTO DE ALTOS ESTUDIOS NACIONALESrepositorio.iaen.edu.ec/bitstream/24000/4004/1/Sangoluisa...e OS-34 1 e 2007 ( ( e e e e e ( e e e e ( ( e e e e e e e e e e e e e e e e ~ROPIEDAD

Documents
Y 8 T r 2 ;I N 9 U O Bonl e C Elementary Bonl e n 222 i · 2020-05-27 · E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

Y 8 T r 2 ;I N 9 U O Bonl e C Elementary Bonl e n 222 i · 2020-05-27 · E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

Documents
Map Sheet 32 - Nebraska Game and Parks Commissionoutdoornebraska.gov/wp-content/uploads/2020/10/Map-Sheet...EE E E E E E EE E E E E EE E E E E E E E E E E EE E EEE E E E E E E E E

Map Sheet 32 - Nebraska Game and Parks Commissionoutdoornebraska.gov/wp-content/uploads/2020/10/Map-Sheet...EE E E E E E EE E E E E EE E E E E E E E E E E EE E EEE E E E E E E E E

Documents
& /RFULDQ 6FDOH · 5 e e e e e e 5 e e e e e e 5 e e e e e e 5 e e e e e e 5 5 e e e e e e 5 e e e e e e 5 e e e e e e 5 e e e e e e 5 e e e e e e 5 5 e e 5 e

& /RFULDQ 6FDOH · 5 e e e e e e 5 e e e e e e 5 e e e e e e 5 e e e e e e 5 5 e e e e e e 5 e e e e e e 5 e e e e e e 5 e e e e e e 5 e e e e e e 5 5 e e 5 e

Documents
Cooper Creek Site Plan Map Cedar Ltd. Salisbury Creek 405-1...e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Cooper Creek Site Plan Map Cedar Ltd. Salisbury Creek 405-1...e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Documents
R u r alI nd st i Zo e Rural Zone Designation...E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

R u r alI nd st i Zo e Rural Zone Designation...E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

Documents
D76 - South Taranaki District · 2021. 1. 20. · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

D76 - South Taranaki District · 2021. 1. 20. · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Documents
E E E E E E E E E E E E E E E E E E E E E E E E ... - Tordera · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

E E E E E E E E E E E E E E E E E E E E E E E E ... - Tordera · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Documents
JRLeon Discovering Geometry Chapter 5.3 HGSH In this chapter you will ● study properties of convex polygons ● discover relationships among their angles,

JRLeon Discovering Geometry Chapter 5.3 HGSH In this chapter you will ● study properties of convex polygons ● discover relationships among their angles,

Documents
2€¦ · d n l-d n - l e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

2€¦ · d n l-d n - l e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Documents
Map Sheet 33 - Nebraska Game and Parks Commission · 78 e ee e e e e e e e e e e e e e e e e ee e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Map Sheet 33 - Nebraska Game and Parks Commission · 78 e ee e e e e e e e e e e e e e e e e ee e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Documents
e-. .-e - Stanford Universityfcic-static.law.stanford.edu/cdn_media/fcic-docs... · • ..•• -•• -e .• -e-•• e e-. e-e-e .e-e e-e e-e .-•..• e-e e-e e-e_e.e_e .-e

e-. .-e - Stanford Universityfcic-static.law.stanford.edu/cdn_media/fcic-docs... · • ..•• -•• -e .• -e-•• e e-. e-e-e .e-e e-e e-e .-•..• e-e e-e e-e_e.e_e .-e

Documents
P Alvesta 14:51 m.fl. · Ø l Øl e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e) 5,0 m1 e1 1500 sk!!!!! ! !!!!! !!!!!

P Alvesta 14:51 m.fl. · Ø l Øl e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e) 5,0 m1 e1 1500 sk!!!!! ! !!!!! !!!!!

Documents
E E E E E E E

E E E E E E E

Documents
JRLeon Geometry Chapter 10.1 HGSH The Geometry of Solids 10.1 Most of the geometric figures you have worked with so far have been flat plane figures with

JRLeon Geometry Chapter 10.1 HGSH The Geometry of Solids 10.1 Most of the geometric figures you have worked with so far have been flat plane figures with

Documents
JRLeon Discovering Geometry Chapter 3.7 HGSH You now can perform a number of constructions in triangles, including angle bisectors, perpendicular bisectors

JRLeon Discovering Geometry Chapter 3.7 HGSH You now can perform a number of constructions in triangles, including angle bisectors, perpendicular bisectors

Documents
18 etfo rs iè 19 - Parispluenligne.paris.fr/plu/sites-plu/site_statique_41/documents/866_Pla… · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

18 etfo rs iè 19 - Parispluenligne.paris.fr/plu/sites-plu/site_statique_41/documents/866_Pla… · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Documents
Z - 2 - Gobapp.sni.gob.ec/sni-link/sni/PORTAL_SNI_2016/sismos/... · 2019-03-05 · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Z - 2 - Gobapp.sni.gob.ec/sni-link/sni/PORTAL_SNI_2016/sismos/... · 2019-03-05 · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Documents
e~E~E~:::~B~e~e~e~e~e~;;~=~=~?e~~e

e~E~E~:::~B~e~e~e~e~e~;;~=~=~?e~~e

Documents
Ionic Bonding Electron Transfer e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e-

Ionic Bonding Electron Transfer e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e-

Documents
AD MI NS TR OC U LE - Habscht · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

AD MI NS TR OC U LE - Habscht · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Documents
Map Sheet 15 Visit OutdoorNebraska.org/PublicAccessAtlas ...outdoornebraska.gov/.../08/2020-21PAAMapsheet_15.pdf · 44 45 e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Map Sheet 15 Visit OutdoorNebraska.org/PublicAccessAtlas ...outdoornebraska.gov/.../08/2020-21PAAMapsheet_15.pdf · 44 45 e e e e e e e e e e e e e e e e e e e e e e e e e e e e e

Documents
e e e e e e e e e e e e e e e e e e e 2015-2016 · e e e e e e e e e e e e e e e e e e e Winter sports previeW Thursday, December 3, 2015 • e e e e 2 2015-2016 Park High RANGERS

e e e e e e e e e e e e e e e e e e e 2015-2016 · e e e e e e e e e e e e e e e e e e e Winter sports previeW Thursday, December 3, 2015 • e e e e 2 2015-2016 Park High RANGERS

Documents
JRLeon Geometry Chapter 8.6 HGSH Lesson 8.6 In Lesson 8.5, you discovered a formula for calculating the area of a circle. With the help of your visual

JRLeon Geometry Chapter 8.6 HGSH Lesson 8.6 In Lesson 8.5, you discovered a formula for calculating the area of a circle. With the help of your visual

Documents
 · be inch'ded not scale-r figures in mm . mill E . E E E E E > E E E E E a E > E E e . E E E e E . E E > E E E e E > E E . Created Date: 4/13/2016 12:24:43 PM

 · be inch'ded not scale-r figures in mm . mill E . E E E E E > E E E E E a E > E E e . E E E e E . E E > E E E e E > E E . Created Date: 4/13/2016 12:24:43 PM

Documents
~e e AFSCME · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e AGREEMENT BETWEEN THE BOARD OF EDUCATION OF LIVONIA PUBLIC SCHOOLS SCHOOL DISTRICT …

~e e AFSCME · e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e AGREEMENT BETWEEN THE BOARD OF EDUCATION OF LIVONIA PUBLIC SCHOOLS SCHOOL DISTRICT …

Documents
e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- 1s 2s 2p 3s 3p Energy Sodium e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e-

e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- 1s 2s 2p 3s 3p Energy Sodium e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e-

Documents
Joint Fuel - Forest Fire Management Victoria - Forest Fire ...€¦ · E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

Joint Fuel - Forest Fire Management Victoria - Forest Fire ...€¦ · E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

Documents