Basic Proportionality Theorem
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Objectives:
- 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
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