SlideShare a Scribd company logo
1 of 16
Proving Triangles Congruent
Two geometric figures with exactly the  same size and shape. The Idea of a Congruence A C B D E F
How much do you  need to know. . . . . . about two triangles  to prove that they  are congruent?
Corresponding Parts ๏„ ABC  ๏€   ๏„   DEF B A C E D F ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Side-Side-Side (SSS) ,[object Object],[object Object],[object Object],๏„ ABC  ๏€   ๏„   DEF E D F If all three sides of one triangle are  congruent to three sides of another triangle,  then the triangles are congruent. B A C
Side-Angle-Side (SAS) ,[object Object],[object Object],[object Object],๏„ ABC  ๏€   ๏„   DEF B A C E D F included  angle
The angle  between  two sides Included Angle
Name the  included  angle: Y E  and  E S E S  and Y S Y S and  Y E Included Angle ๏ƒ   E ๏ƒ   S ๏ƒ   Y S Y E
The Congruence Postulates ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Name That Postulate SAS SSS SSA (when possible)
Name That Postulate (when possible) SAS AAA SSA
Name That Postulate (when possible) SAS SAS SAS Reflexive Property Vertical Angles Vertical Angles Reflexive Property SSA
You try! Name That Postulate (when possible)
(when possible) You try! Name That Postulate
Indicate the additional information needed to enable us to apply the specified congruence postulate. For SAS:
Point X is the midpoint of AE and BD. 1. Which segments are congruent? 2. Why is <1 congruent to <2? 3. Why is triangle ACB congruent to triangle ECD?

More Related Content

What's hot

4-1 Corresponding Parts In A Congruence
4-1 Corresponding Parts In A Congruence4-1 Corresponding Parts In A Congruence
4-1 Corresponding Parts In A Congruence
Mr. Hohman
ย 
Triangle-Congruence-Postulate-Day-4.pptx
Triangle-Congruence-Postulate-Day-4.pptxTriangle-Congruence-Postulate-Day-4.pptx
Triangle-Congruence-Postulate-Day-4.pptx
mikeebio1
ย 
7-2 Exterior Angle Theorem
7-2 Exterior Angle Theorem7-2 Exterior Angle Theorem
7-2 Exterior Angle Theorem
mgngallagher
ย 
Triangle congruence
Triangle congruenceTriangle congruence
Triangle congruence
jbianco9910
ย 

What's hot (20)

trapezoid and its properties
trapezoid and its propertiestrapezoid and its properties
trapezoid and its properties
ย 
Congruent figure
Congruent figureCongruent figure
Congruent figure
ย 
Proportionality theorem and its converse
Proportionality theorem and its converseProportionality theorem and its converse
Proportionality theorem and its converse
ย 
2.6.3 Congruent Triangle Proofs
2.6.3 Congruent Triangle Proofs2.6.3 Congruent Triangle Proofs
2.6.3 Congruent Triangle Proofs
ย 
Triangle Congruence (Introduction)
Triangle Congruence (Introduction)Triangle Congruence (Introduction)
Triangle Congruence (Introduction)
ย 
Corresponding parts of congruent figures.
Corresponding parts of congruent figures.Corresponding parts of congruent figures.
Corresponding parts of congruent figures.
ย 
Congruent triangles
Congruent trianglesCongruent triangles
Congruent triangles
ย 
Module-4-Presentation.pptx
Module-4-Presentation.pptxModule-4-Presentation.pptx
Module-4-Presentation.pptx
ย 
ASA, SAS,AAS,SSS
ASA, SAS,AAS,SSSASA, SAS,AAS,SSS
ASA, SAS,AAS,SSS
ย 
Introduction to Postulates and Theorems
Introduction to Postulates and TheoremsIntroduction to Postulates and Theorems
Introduction to Postulates and Theorems
ย 
Basic proportionality theorem
Basic proportionality theoremBasic proportionality theorem
Basic proportionality theorem
ย 
4-1 Corresponding Parts In A Congruence
4-1 Corresponding Parts In A Congruence4-1 Corresponding Parts In A Congruence
4-1 Corresponding Parts In A Congruence
ย 
4.3-5 Triangle Congruence
4.3-5 Triangle Congruence4.3-5 Triangle Congruence
4.3-5 Triangle Congruence
ย 
GRADE 8-ILLUSTRATING THE SAS, ASA AND SSS.pptx
GRADE 8-ILLUSTRATING THE SAS, ASA AND SSS.pptxGRADE 8-ILLUSTRATING THE SAS, ASA AND SSS.pptx
GRADE 8-ILLUSTRATING THE SAS, ASA AND SSS.pptx
ย 
Triangle-Congruence-Postulate-Day-4.pptx
Triangle-Congruence-Postulate-Day-4.pptxTriangle-Congruence-Postulate-Day-4.pptx
Triangle-Congruence-Postulate-Day-4.pptx
ย 
Theorem on similarity
Theorem on similarityTheorem on similarity
Theorem on similarity
ย 
7-2 Exterior Angle Theorem
7-2 Exterior Angle Theorem7-2 Exterior Angle Theorem
7-2 Exterior Angle Theorem
ย 
Triangle congruence
Triangle congruenceTriangle congruence
Triangle congruence
ย 
2.5.6 Perpendicular and Angle Bisectors
2.5.6 Perpendicular and Angle Bisectors2.5.6 Perpendicular and Angle Bisectors
2.5.6 Perpendicular and Angle Bisectors
ย 
2.5.4 Hinge Theorem
2.5.4 Hinge Theorem2.5.4 Hinge Theorem
2.5.4 Hinge Theorem
ย 

Viewers also liked (8)

4.3 proving triangles are congruent
4.3 proving triangles are congruent4.3 proving triangles are congruent
4.3 proving triangles are congruent
ย 
Ibong adarna copy
Ibong adarna   copyIbong adarna   copy
Ibong adarna copy
ย 
Ikalawang digmaang-pandaigdig
Ikalawang digmaang-pandaigdigIkalawang digmaang-pandaigdig
Ikalawang digmaang-pandaigdig
ย 
Ibong adarna ppt
Ibong adarna pptIbong adarna ppt
Ibong adarna ppt
ย 
Ibong adarna
Ibong adarnaIbong adarna
Ibong adarna
ย 
Ikalawang Digmaang Pandaigdig
Ikalawang Digmaang PandaigdigIkalawang Digmaang Pandaigdig
Ikalawang Digmaang Pandaigdig
ย 
Ibong adarna
Ibong adarnaIbong adarna
Ibong adarna
ย 
IKALAWANG DIGMAANG PANDAIGDIG
IKALAWANG DIGMAANG PANDAIGDIGIKALAWANG DIGMAANG PANDAIGDIG
IKALAWANG DIGMAANG PANDAIGDIG
ย 

Similar to TechMathI - 4.1 - Congruent Triangles

Provingtrianglescongruentssssasasa
ProvingtrianglescongruentssssasasaProvingtrianglescongruentssssasasa
Provingtrianglescongruentssssasasa
Jessica Garcia
ย 
Provingtrianglescongruentssssasasa
ProvingtrianglescongruentssssasasaProvingtrianglescongruentssssasasa
Provingtrianglescongruentssssasasa
Jessica Garcia
ย 
10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt
DianaJanicaMagalong2
ย 
10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt
Marjorie Malveda
ย 
10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt
mikeebio1
ย 
Geometrycongruence
GeometrycongruenceGeometrycongruence
Geometrycongruence
Tholene Wongyu
ย 
11X1 T08 03 congruent triangles (2011)
11X1 T08 03 congruent triangles (2011)11X1 T08 03 congruent triangles (2011)
11X1 T08 03 congruent triangles (2011)
Nigel Simmons
ย 
11X1 T07 03 congruent triangles (2010)
11X1 T07 03 congruent triangles (2010)11X1 T07 03 congruent triangles (2010)
11X1 T07 03 congruent triangles (2010)
Nigel Simmons
ย 
11 x1 t07 03 congruent triangles (2012)
11 x1 t07 03 congruent triangles (2012)11 x1 t07 03 congruent triangles (2012)
11 x1 t07 03 congruent triangles (2012)
Nigel Simmons
ย 
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
AngelaCamillePaynant
ย 
Congruence of Triangle
Congruence of TriangleCongruence of Triangle
Congruence of Triangle
itutor
ย 

Similar to TechMathI - 4.1 - Congruent Triangles (20)

Provingtrianglescongruentssssasasa
ProvingtrianglescongruentssssasasaProvingtrianglescongruentssssasasa
Provingtrianglescongruentssssasasa
ย 
Geometry congruence
Geometry congruenceGeometry congruence
Geometry congruence
ย 
K to 12 Grade 9 Math geometry congruence.pptx
K to 12 Grade 9 Math geometry congruence.pptxK to 12 Grade 9 Math geometry congruence.pptx
K to 12 Grade 9 Math geometry congruence.pptx
ย 
Geometrycongruence
GeometrycongruenceGeometrycongruence
Geometrycongruence
ย 
proving triangles are congruent
proving triangles are congruentproving triangles are congruent
proving triangles are congruent
ย 
proving triangles are congruent.docx
proving triangles are congruent.docxproving triangles are congruent.docx
proving triangles are congruent.docx
ย 
provingtrianglescongruentssssasasa-091123170916-phpapp01.ppt
provingtrianglescongruentssssasasa-091123170916-phpapp01.pptprovingtrianglescongruentssssasasa-091123170916-phpapp01.ppt
provingtrianglescongruentssssasasa-091123170916-phpapp01.ppt
ย 
proving-triangles-are-congruent.ppt
proving-triangles-are-congruent.pptproving-triangles-are-congruent.ppt
proving-triangles-are-congruent.ppt
ย 
Provingtrianglescongruentssssasasa
ProvingtrianglescongruentssssasasaProvingtrianglescongruentssssasasa
Provingtrianglescongruentssssasasa
ย 
10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt
ย 
10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt
ย 
10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt10.17 Triangle Congruence Proofs Day 2.ppt
10.17 Triangle Congruence Proofs Day 2.ppt
ย 
congruenttriangles-130611002549-.docx
congruenttriangles-130611002549-.docxcongruenttriangles-130611002549-.docx
congruenttriangles-130611002549-.docx
ย 
Geometrycongruence
GeometrycongruenceGeometrycongruence
Geometrycongruence
ย 
11X1 T08 03 congruent triangles (2011)
11X1 T08 03 congruent triangles (2011)11X1 T08 03 congruent triangles (2011)
11X1 T08 03 congruent triangles (2011)
ย 
11X1 T07 03 congruent triangles (2010)
11X1 T07 03 congruent triangles (2010)11X1 T07 03 congruent triangles (2010)
11X1 T07 03 congruent triangles (2010)
ย 
11 x1 t07 03 congruent triangles (2012)
11 x1 t07 03 congruent triangles (2012)11 x1 t07 03 congruent triangles (2012)
11 x1 t07 03 congruent triangles (2012)
ย 
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
ย 
Congruence of Triangle
Congruence of TriangleCongruence of Triangle
Congruence of Triangle
ย 
Geometrycongruence opt
Geometrycongruence optGeometrycongruence opt
Geometrycongruence opt
ย 

More from lmrhodes

Geo cheat sheet
Geo cheat sheetGeo cheat sheet
Geo cheat sheet
lmrhodes
ย 
Final review 1
Final review 1Final review 1
Final review 1
lmrhodes
ย 
Poly centers answer sheet
Poly centers answer sheetPoly centers answer sheet
Poly centers answer sheet
lmrhodes
ย 
Polynomial review centers
Polynomial review centersPolynomial review centers
Polynomial review centers
lmrhodes
ย 
TechMathI - Point slope form
TechMathI - Point slope formTechMathI - Point slope form
TechMathI - Point slope form
lmrhodes
ย 
TechMathI - Standard form
TechMathI - Standard formTechMathI - Standard form
TechMathI - Standard form
lmrhodes
ย 
TechMathI - Slope intercept form
TechMathI - Slope intercept formTechMathI - Slope intercept form
TechMathI - Slope intercept form
lmrhodes
ย 
TechMathI - Rate of change and slope
TechMathI - Rate of change and slopeTechMathI - Rate of change and slope
TechMathI - Rate of change and slope
lmrhodes
ย 
TechMathI - Ch6 Test
TechMathI - Ch6 TestTechMathI - Ch6 Test
TechMathI - Ch6 Test
lmrhodes
ย 
TechMathI - Ch6 Review
TechMathI - Ch6 ReviewTechMathI - Ch6 Review
TechMathI - Ch6 Review
lmrhodes
ย 
TechMathI - Ch6 Quiz
TechMathI - Ch6 QuizTechMathI - Ch6 Quiz
TechMathI - Ch6 Quiz
lmrhodes
ย 
TechMathI - 6.2 - Similarity examples
TechMathI - 6.2 - Similarity examplesTechMathI - 6.2 - Similarity examples
TechMathI - 6.2 - Similarity examples
lmrhodes
ย 
TechMathI - 6.2 - Similarity
TechMathI - 6.2 - SimilarityTechMathI - 6.2 - Similarity
TechMathI - 6.2 - Similarity
lmrhodes
ย 
TechMathI - 6.1 - Ratio and Proportion
TechMathI - 6.1 - Ratio and ProportionTechMathI - 6.1 - Ratio and Proportion
TechMathI - 6.1 - Ratio and Proportion
lmrhodes
ย 
TechMathI - Ch5 Test
TechMathI - Ch5 TestTechMathI - Ch5 Test
TechMathI - Ch5 Test
lmrhodes
ย 
TechMathI - Ch5 Vocab Quiz
TechMathI - Ch5 Vocab QuizTechMathI - Ch5 Vocab Quiz
TechMathI - Ch5 Vocab Quiz
lmrhodes
ย 
TechMathI - 5.6 - Trapezoids
TechMathI - 5.6 - TrapezoidsTechMathI - 5.6 - Trapezoids
TechMathI - 5.6 - Trapezoids
lmrhodes
ย 
TechMathI - 5.5 - Special Parallelograms
TechMathI - 5.5 - Special ParallelogramsTechMathI - 5.5 - Special Parallelograms
TechMathI - 5.5 - Special Parallelograms
lmrhodes
ย 
TechMathI - 5.4 - Parallelograms
TechMathI - 5.4 - ParallelogramsTechMathI - 5.4 - Parallelograms
TechMathI - 5.4 - Parallelograms
lmrhodes
ย 
TechMathI - 5.3 - Properties of Quadrilaterals
TechMathI - 5.3 - Properties of QuadrilateralsTechMathI - 5.3 - Properties of Quadrilaterals
TechMathI - 5.3 - Properties of Quadrilaterals
lmrhodes
ย 

More from lmrhodes (20)

Geo cheat sheet
Geo cheat sheetGeo cheat sheet
Geo cheat sheet
ย 
Final review 1
Final review 1Final review 1
Final review 1
ย 
Poly centers answer sheet
Poly centers answer sheetPoly centers answer sheet
Poly centers answer sheet
ย 
Polynomial review centers
Polynomial review centersPolynomial review centers
Polynomial review centers
ย 
TechMathI - Point slope form
TechMathI - Point slope formTechMathI - Point slope form
TechMathI - Point slope form
ย 
TechMathI - Standard form
TechMathI - Standard formTechMathI - Standard form
TechMathI - Standard form
ย 
TechMathI - Slope intercept form
TechMathI - Slope intercept formTechMathI - Slope intercept form
TechMathI - Slope intercept form
ย 
TechMathI - Rate of change and slope
TechMathI - Rate of change and slopeTechMathI - Rate of change and slope
TechMathI - Rate of change and slope
ย 
TechMathI - Ch6 Test
TechMathI - Ch6 TestTechMathI - Ch6 Test
TechMathI - Ch6 Test
ย 
TechMathI - Ch6 Review
TechMathI - Ch6 ReviewTechMathI - Ch6 Review
TechMathI - Ch6 Review
ย 
TechMathI - Ch6 Quiz
TechMathI - Ch6 QuizTechMathI - Ch6 Quiz
TechMathI - Ch6 Quiz
ย 
TechMathI - 6.2 - Similarity examples
TechMathI - 6.2 - Similarity examplesTechMathI - 6.2 - Similarity examples
TechMathI - 6.2 - Similarity examples
ย 
TechMathI - 6.2 - Similarity
TechMathI - 6.2 - SimilarityTechMathI - 6.2 - Similarity
TechMathI - 6.2 - Similarity
ย 
TechMathI - 6.1 - Ratio and Proportion
TechMathI - 6.1 - Ratio and ProportionTechMathI - 6.1 - Ratio and Proportion
TechMathI - 6.1 - Ratio and Proportion
ย 
TechMathI - Ch5 Test
TechMathI - Ch5 TestTechMathI - Ch5 Test
TechMathI - Ch5 Test
ย 
TechMathI - Ch5 Vocab Quiz
TechMathI - Ch5 Vocab QuizTechMathI - Ch5 Vocab Quiz
TechMathI - Ch5 Vocab Quiz
ย 
TechMathI - 5.6 - Trapezoids
TechMathI - 5.6 - TrapezoidsTechMathI - 5.6 - Trapezoids
TechMathI - 5.6 - Trapezoids
ย 
TechMathI - 5.5 - Special Parallelograms
TechMathI - 5.5 - Special ParallelogramsTechMathI - 5.5 - Special Parallelograms
TechMathI - 5.5 - Special Parallelograms
ย 
TechMathI - 5.4 - Parallelograms
TechMathI - 5.4 - ParallelogramsTechMathI - 5.4 - Parallelograms
TechMathI - 5.4 - Parallelograms
ย 
TechMathI - 5.3 - Properties of Quadrilaterals
TechMathI - 5.3 - Properties of QuadrilateralsTechMathI - 5.3 - Properties of Quadrilaterals
TechMathI - 5.3 - Properties of Quadrilaterals
ย 

Recently uploaded

Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
ciinovamais
ย 

Recently uploaded (20)

Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17  How to Extend Models Using Mixin ClassesMixin Classes in Odoo 17  How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
ย 
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsOn National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan Fellows
ย 
Third Battle of Panipat detailed notes.pptx
Third Battle of Panipat detailed notes.pptxThird Battle of Panipat detailed notes.pptx
Third Battle of Panipat detailed notes.pptx
ย 
Sociology 101 Demonstration of Learning Exhibit
Sociology 101 Demonstration of Learning ExhibitSociology 101 Demonstration of Learning Exhibit
Sociology 101 Demonstration of Learning Exhibit
ย 
Unit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxUnit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptx
ย 
Dyslexia AI Workshop for Slideshare.pptx
Dyslexia AI Workshop for Slideshare.pptxDyslexia AI Workshop for Slideshare.pptx
Dyslexia AI Workshop for Slideshare.pptx
ย 
ICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptxICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptx
ย 
Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...
ย 
How to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSHow to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POS
ย 
ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701
ย 
PROCESS RECORDING FORMAT.docx
PROCESS      RECORDING        FORMAT.docxPROCESS      RECORDING        FORMAT.docx
PROCESS RECORDING FORMAT.docx
ย 
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
ย 
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfUGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
ย 
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17
ย 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
ย 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introduction
ย 
Understanding Accommodations and Modifications
Understanding  Accommodations and ModificationsUnderstanding  Accommodations and Modifications
Understanding Accommodations and Modifications
ย 
Food safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfFood safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdf
ย 
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptxBasic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
ย 
Holdier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdfHoldier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdf
ย 

TechMathI - 4.1 - Congruent Triangles