School level

7th May

7th May: Similar Triangles

Learning Outcomes

Students working at LCOL should be able to:

• use the following terms related to logic and deductive reasoning: theorem, proof, axiom, corollary, converse, implies
• investigate theorems 7, 8, 11, 12, 13, 16, 17, 18, 20, 21 and corollary 6 and use them to solve problems

Students working at LCHL should be able to:

• prove theorems 11,12,13, concerning ratios which lay the proper foundation for the proof of the theorem of Pythagoras studied at junior cycle

Prior Learning
Theorems
Connections
SEC Exam Questions

Vertically- Opposite Angles - Instructional Video

https://www.youtube.com/watch?v=oOTGSKtZ1dM Added: 10 May 2018 Contributor: PDST Resource type: Demonstration / Audio / Video

This video although entitled “Vertically Opposite Angles”, it can be used for all areas of geometry as appropriate. It comes in two sections:
Section 1:
• Discovery Learning in Geometry
• Good Questioning

Section 2:
• Generalising through questioning
• Algebra as Sense making

JC Mathematics

How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 3. Geometrical Proof

Suggestions for use: used to help students discover that vertically opposite angles are equal

Key Skills: Being Creative Communicating Managing Information and Thinking Working with Others

Asset type: Video
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

Angles

https://youtu.be/intrPF3I4To Added: 20 Jun 2018 Contributor: UCD MSC Resource type: Audio / Video

Review important JC Geometry concepts using this 3-minute video clip. The video clip reviews the terms vertically opposite angles, alternate angles and corresponding angles. This video was produced by the UCD Maths Support Centre in conjunction with UCD access centre.

SC Mathematics
JC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 3. Geometrical Proof

Asset type: Video
Language: English
Special Needs:

Theorems in your own words jchl

https://www.scoilnet.ieuploads/resources/28367/28103.pdf Added: 17 Sep 2018 Contributor: PDST Resource type: Assessment / Worksheet

Putting theorems into your own words Junior Certificate Higher level
An interesting activity to enable students to become familiar with theorems. Used to foster a deeper understanding of the theorems among the learners.

JC Mathematics

How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 3. Geometrical Proof

Suggestions for use: An activity to enable students to become familiar with theorems. Used to foster a deeper understanding of the theorems among the learners.

Key Skills: Communicating Managing Information and Thinking Literacy Numeracy

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

Functions Axioms, Theorems and Corollaries

https://www.scoilnet.ie/pdst/maths/...ometry/axioms-theorems-corollaries/ Added: 03 Jul 2019 Contributor: PDST Resource type: Guide/notes / Simulation

GeoGebra files on all of the Junior Cycle theorems,
Note: The specification states that Junior Cycle students should be able to: b) recall and use the concepts, axioms, theorems, corollaries and converses, specified in Geometry for Post-Primary School Mathematics (section 9 for OL and section 10 for HL) i.) axioms 1, 2, 3, 4 and 5 ii.) theorems 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 15 and 11, 12, 19, and appropriate converses, including relevant operations involving square roots iii.) corollaries 3, 4 and 1, 2, 5 and appropriate converses.

JC Mathematics

How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 3. Geometrical Proof

Asset type: Online Resource
Language: English
Special Needs:

Introducing Similar Triangles - student activity

https://www.projectmaths.ie/documen...roducingSimilarTriangles.pdf?strand Added: 06 May 2020 Contributor: PDST Resource type: Worksheet

This worksheet allows students to construct and explore the properties of similar triangles.

JC Mathematics

How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 3. Geometrical Proof

Suggestions for use: Give to students to use with correct geometric equipment and discover the properties and ratios of similar triangles.

Asset type: Document
Language: English
Special Needs:

Axioms, Theorems and Corollaries - Leaving Certificate

https://www.scoilnet.ie/pdst/maths/.../lc/geometry-trigonometry/theorems/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

Interactive Geogebra files and student worksheets for the Leaving Cert Theorems 7-8, 11-13 and 16-21.

SC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Asset type: Online Resource
Language: English
Special Needs:

Similar Triangles - Theorem

https://youtu.be/uFvnScBlAbk Added: 20 Jun 2018 Contributor: UCD MSC Resource type: Audio / Video

Develop students understanding of similar triangles with this 4-minute video clip. Video explains theorem 13. This video was produced by the UCD Maths Support Centre in conjunction with UCD access centre.

SC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Suggestions for use: Flipped learning - Assign the video as a homework task. Students watch the video at home and can then apply what they learned in the next lesson.

Asset type: Video
Language: English
Special Needs:

Theorems in your own words LCOL

https://www.projectmaths.ie/documen...eoremsInYourOwnWordsLCOL.pdf?strand Added: 06 May 2020 Contributor: PDST Resource type: Worksheet

Worksheets on theorems to encourage students to explore the theorems in their own words.

SC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Suggestions for use: Worksheet to give to students to guide them to a deeper understanding on theorems

Asset type: Document
Language: English
Special Needs:

Theorems in your own words LCHL

https://www.projectmaths.ie/documen...eoremsInYourOwnWordsLCHL.pdf?strand Added: 06 May 2020 Contributor: PDST Resource type: Worksheet

Worksheet containing a table of the LCHL theorems with spaces left for students to provide descriptions in their own words.

SC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Suggestions for use: Give this worksheet to students to encourage a deeper understanding of the theorems at LCHL

Asset type: Document
Language: English
Special Needs:

Constructions - Leaving Certificate

https://www.scoilnet.ie/pdst/maths/...eometry-trigonometry/constructions/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

Interactive Geogebra files and students worksheets demonstrating the Leaving Cert Constructions 16 - 22.

SC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Asset type: Online Resource
Language: English
Special Needs:

Interactive Geometry Quiz

https://www.scoilnet.ieuploads/resources/28368/28104.ppt Added: 17 Sep 2018 Contributor: PDST Resource type: Assessment / Presentation

A Geometry quiz to use with the whole class or see teams of students try to be the best. Will they play safe with a 10 point question or risk all on a 50 point one. Bonus points abound for those who dare win!

JC Mathematics

How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 3. Geometrical Proof

Suggestions for use: A Geometry quiz to use with the whole class or see teams of students try to be the best. Will they play safe with a 10 point question or risk all on a 50 point one. Bonus points abound for those who dare win!

Key Skills: Communicating Managing Information and Thinking Working with Others Literacy Numeracy Managing Myself

Asset type: Presentation
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

Congruent Triangles

https://youtu.be/O-Khn1hEPsA Added: 20 Jun 2018 Contributor: UCD MSC Resource type: Audio / Video

Get students to consider what constitutes a congruent triangle with this 6-minute introductory video. The video walks through the 4 ways to prove that a triangle is a congruent triangle. (SSS, SAS, RHS, ASA )This video was produced by the UCD Maths Support Centre in conjunction with UCD access centre.

SC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Suggestions for use: Flipped learning - Assign the video as a homework task. Students watch the video at home and can then apply what they learned in the next lesson.

Asset type: Video
Language: English
Special Needs:

SEC 2018 LCOL P2 Q2

SEC past exam question to assess understanding of similar triangles.

SC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Suggestions for use: SEC past exam question

Asset type: Document
Language: English
Special Needs:

SEC 2015 LCOL P2 Q4

SEC past exam question to assess understanding of similar triangles.

SC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Suggestions for use: SEC past exam question

Asset type: Document
Language: English
Special Needs:

SEC 2019 LCHL P2 Q5

SEC past exam question to assess understanding of similar triangles

SC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Suggestions for use: SEC past exam question

Asset type: Document
Language: English
Special Needs:

SEC 2017 LCHL P2 Q5

SEC past exam question to assess understanding of similar triangles

SC Mathematics

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Suggestions for use: SEC past exam question

Asset type: Document
Language: English
Special Needs:

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