Mathomat V3

# Construct a Perpendicular through a Point on a Line

video tutorial part
5
of

## Learning Geometry with a Circle Arc Template

with

### Chris Tisdell

Mathematician & Educator

### Materials you will need:

Mathomat V3 Template
Unlined Paper / Scrap Paper
Sharp Pencil/s
Fine-point Pen/s
Eraser

### What you will learn in this tutorial:

In this presentation, Chris Tisdell delves into the world of geometric construction, specifically focusing on the use of a circle arc template as a versatile tool that can replace traditional compasses in geometry education. The circle arc template, which is part of a larger mathematical tool, offers greater accuracy and safety when drawing circle arcs. Tisdell begins by introducing the audience to this critical tool.

He shares his screen, revealing the circle arc template, its markings, and its unique capabilities. The tool allows for precise positioning of circle arcs by aligning its centre with a designatedpoint and using a straight edge in conjunction. Tisdell emphasises that while the template contains various markings, not all of them are necessary for theconstructions he demonstrates.

The main geometric problem explored in this presentation involves constructing a perpendicular line segment to a given line segment that passes through a specified point on the given segment. This is a classic problem in geometry that has been studied for centuries. The challenge here is to achieve this construction accurately and safely, which is where the circle arc template comes into play.

Tisdell begins by drawing a line segment AB and labelling its endpoints as A and B. He aims to construct a line perpendicular to AB through a point C located on AB. To demonstrate this, he uses the circle arc template to draw an extended arc that intersects AB at two new points, D and E. The midpoint of DE, labeled as C, serves as the desired point of intersection for the perpendicular line segment.

The construction of an equilateral triangle with DE as its base is the next step in solving this problem. Tisdell refers to a previous video where he demonstrated how to construct an equilateral triangle with a given base using the same circle arc template and straight edge.However, in this case, he wants to create the equilateral triangle with base AB instead.

Using the circle arc template, Tisdell carefully constructs two arcs from points D and E, each intersecting the other side of DE. These intersections yield two new points, F and G, completing the equilateral triangle with base DE.

To ensure the perpendicularity of the constructed line segment IC to AB, Tisdell points out that triangle CGE and triangle CIF are congruent by side-side-side congruence. This congruence demonstrates that angle DCI is equal to angle ECI, thereby proving that line segment IC is indeed perpendicular to AB at point C.

In summary, Chris Tisdell's presentation showcases the utility of the circle arc template in solving classic geometric problems with precision and safety. His step-by-step construction of a perpendicular line segment through a given point on a line segment serves as an excellent example of how this tool can enhance geometry education and geometric problem-solving.

### Chris Tisdell

Mathematician & Educator
Chris, a mathematician and educator, is an academic advisor to Mathomat. Chris approached us in 2021 with an interest in the circle templates in Mathomat...
Online Store

### Purchase some of our most popular products from the official Mathomat online store

#### Finding Hidden Angles, a Mathomat Adventure

##### V7 template with 48 page student book
Template
\$
19.95
Use Mathomat with the finding hidden angles student book. Gain insight into the geometry of the world by understanding angle. Build confidence with maths.

#### Mathomat V7 Builder Pack

##### with 96 page student manual
Template
\$
19.95
The Mathomat V7 template with an illustrated manual of investigations that familiarise students with the use of Mathomat for creative drawing.

#### Mathomat V7 Explorer Pack

##### Template & 72 page student manual
Template
\$
19.95
The Mathomat V7 geometry template with 72 page illustrated student manual and MAC guide by Juliet Snape. Illustrated contexts for student directed learning.

#### Geometry & Beyond

##### with Mathomat
Publication
\$
24.95
A series of lessons for secondary school which make use of available classroom materials, such as the Mathomat template and geometry software.

#### Maths with Mathomat

##### Lesson Plans Years 4-9 & Beyond
Publication
\$
24.95
A series of comprehensive lesson plans developed to give teachers a glimpse of the potential for using Mathomat as an aid in the teaching of mathematics.

#### Text Book & Units of Work

##### with Mathomat
Publication
\$
24.95
This 116 page book of investigations with Mathomat reveal the passion for teaching of Craig Young, the designer of the original Mathomat.
01

### Lesson Plans

#### Learn to teach maths with Mathomat

Get a glimpse of the tremendous potential for using Mathomat as an aid to teaching mathematics.

02

### Video Tutorials

#### Watch and learn from Pr. Chris Tisdell

Using a series of Mathomat products and templates, learn maths and geometry with Pr. Chris Tisdell.

03

### Online Store

#### Visit the official Mathomat store

Purchase official Mathomat templates, booklets and teaching resources for your child or classroom.

04