Basic Proportionality Theorem

Objectives:

1. Familiarity with idea of congruence, similarity and similar triangles
2. 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.
3. Logical proof of BPT

Session plan:

1. Congruence
   1. Segment, angle, triangle, quadrilateral, odd shaped figures
   2. Measures of corresponding sides and angles of congruent polygons will be equal
2. Similarity
   1. Any circle is similar to any other circle.
   2. Same holds for Square - https://geogebra.org/m/ceapgrs5
   3. and Equilateral Triangles and https://geogebra.org/m/kpww6afy
   4. Quadrilaterals
      1. Two quadrilaterals of the same number of sides are similar, if
         1. (i) their corresponding angles are equal and
         2. (ii) their corresponding sides are in the same ratio (or proportion)
   5. Triangle - https://geogebra.org/m/mdc43fbt
      1. if all angles of one are congruent with the corresponding angles of the second (AAA)
      2. if the ratio of three corresponding sides are equal (SSS)
3. Concept of height of a triangle. https://geogebra.org/m/k56qc3hm
   1. 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)
   2. Selection of side as base can change, but area (half * base *height) does not change
4. 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.
   1. Draw few triangles and check that this is true – visual proof https://geogebra.org/m/nctk4smk
   2. Logical Proof of BPT - https://geogebra.org/m/pjdj65cd