1. This document provides teaching materials for two concepts in geometry: vertically opposite angles and tangents drawn from an external point to a circle. 2. For vertically opposite angles, the material includes a cardboard covered in chart paper with a printed protractor and movable straws to demonstrate that vertically opposite angles are always equal. 3. For tangents drawn from an external point, the material includes drawing a circle on cardboard, attaching movable straws from an external point to act as tangents, and showing that the lengths of the tangents are equal.

1. TEACHING LEARNING MATERIAL
1-VERTICALLY OPPOSITE ANGLES
2-TANGENTS DRAWNFROM AN EXTERNAL POINT TO A
CIRCLE ARE EQUAL IN LENGTH
Concept 1: Vertically opposite angles are always equal
Objectives: To learn about vertically opposite angles.
Material Required: Cardboard, chart paper, wooden nail, printed
protector, straws, stapler, etc.
Method of Construction:
• Take a cardboard and covered it with chart paper.
• cover it with white chart paper and glue to it printed protractor
• Take two straws and make a V and put pins at appropriate places.
• Take two coloured papers and stick them by cutting into four
sectors think like making a big circle and cutting it into four equal
pieces.
Application in the Classroom:
• Your straws are free to move and just hold one and move others
at the same time.
• When you move and now leave, we can see two angles which are
vertically opposite to each other

2. • With the help of printed protractor, we can measure the two
angles
• We can see that the two vertically opposite angles are always
equal which proves the

5. Concept 2: Tangents drawn from an external point to a circle are equal
in length.
Objectives: To learn the length of tangents drawn from one external
point to the circle.
Material Required: Cardboard, chart paper, wooden nail, straws,
stapler, etc.
Method of Construction:
• Take a cardboard and covered it with chart paper
• Draw a circle of the appropriate radius on it
• Take an external point and we need to draw two tangents to the
given circle
• So we take two straws and cut them in such a way that their
length equals the length of the tangents drawn to the circle
• We fix the two straws with the help of wooden nail on the
external point

6. Application in the Classroom:
• Your straws are free to move and just move both at the same
time so they become tangent to the given circle.
• Now at the points where these straws touch the circle, we mark
with the help of a permanent marker

7. • Now we bring both the straws close to each other and we find
that both the points coincide which shows that the length is equal