# District Maths Teachers Workshop Feb 21

From Karnataka Open Educational Resources

Bengaluru South DIET Mathematics online course - Demonstration and hands-on Geogebra to teach BPT and Frustum

## Contents

### Objectives of workshop

- Familiarity with idea of congruence, similarity and similar triangles
- Visualizing BPT - If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. Logical proof of BPT
- Visualizing area of Frustum of a Cone (3D)

### Improve display of Geogebra on your phone

- Use in landscape mode
- Full screen our presentation
- Desktop option on phone
- If in difficulty, simply refresh the screen.

### Session plan

- Congruence
- Segment, angle, triangle, quadrilateral, odd shaped figures
- Measures of corresponding sides and angles of congruent polygons will be equal

- Similarity
- Any circle is similar to any other circle.
- Same holds for Square - https://geogebra.org/m/ceapgrs5
- and Equilateral Triangles and https://geogebra.org/m/kpww6afy
- Quadrilaterals
- Two quadrilaterals of the same number of sides are similar, if
- (i) their corresponding angles are equal and
- (ii) their corresponding sides are in the same ratio (or proportion)

- Two quadrilaterals of the same number of sides are similar, if
- Triangle - https://geogebra.org/m/mdc43fbt
- if all angles of one are congruent with the corresponding angles of the second (AAA)
- if the ratio of three corresponding sides are equal (SSS)

- Concept of height of a triangle. https://geogebra.org/m/k56qc3hm
- The height of a triangle will be inside the triangle (acute angled triangle), outside the triangle (obtuse angled triangle) and on the side of the triangle (right triangle)
- Selection of side as base can change, but area (half * base *height) does not change

- BPT - If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
- Draw few triangles and check that this is true – visual proof https://geogebra.org/m/nctk4smk
- Logical Proof of BPT - https://geogebra.org/m/pjdj65cd

### Time plan

- Introduction to http://geogebra.org. Enable ‘Desktop view' and 'Landscape view' on phone – 15 minutes
- Demo and hands-on - Congruence – 15 minutes, Similarity 20 minutes. BPT 20 minutes. Frustum of Cone – 10 minutes
- Closing way forward + Google form – 10 minutes.

### General Instructions for using the files

- Open Geogebra.org and login with id
**Ganithageogebra, password - geogebra123** - You can click on the link to open the file (or folder) on your computer or phone with Internet connectivity
- You can move the objects to coincide with the other object, by selecting the object and using ‘drag and drop’ of your mouse/cursor.
- You can also move the object by move the red point and rotating with the yellow point on an object.
- Practice drag and drop using mouse cursor on the computer and your finger on your phone.
- Use the file in the sequence of “check boxes” (Tick mark off/ on)
- Check box – click on it to ON. Click again to OFF
- When needed, move the “Slider” – Move to increase or reduce value of variable (like audio volume control)
- Uncheck a check-box when not needed or to reduce information on the screen
- You can download the file to your own computer, see the steps given in video https://youtu.be/ECFKjQXT6IE (see from 1.40 to 2.00 minutes)
- You can install Geogebra on your computer having Microsoft Windows and also on your android phone, through Google play (Geometry app)
- You can show in your class using the Geogebra on your computer, or if you have connectivity, directly from the website, connecting to projector.
- Students can also see and play with these files on their own phone or using the computer lab.

### Access Geogebra resources

You can open the link in the table below on your computer or your phone

**To learn more about Geogebra visit the Learn Geogebra page**

To Download this page click here