Difference between revisions of "Basic Proportionality Theorem"
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(Created page with "=== Objectives: === === Session plan: === === Assessment: ===") |
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=== Objectives: === | === 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: === | === 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 - <nowiki>https://geogebra.org/m/ceapgrs5</nowiki> | ||
+ | ## and Equilateral Triangles and <nowiki>https://geogebra.org/m/kpww6afy</nowiki> | ||
+ | ## 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) | ||
+ | ## Triangle - <nowiki>https://geogebra.org/m/mdc43fbt</nowiki> | ||
+ | ### 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. <nowiki>https://geogebra.org/m/k56qc3hm</nowiki> | ||
+ | ## 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 <nowiki>https://geogebra.org/m/nctk4smk</nowiki> | ||
+ | ## Logical Proof of BPT - <nowiki>https://geogebra.org/m/pjdj65cd</nowiki> | ||
=== Assessment: === | === Assessment: === | ||
+ | [[Category:Triangles]] | ||
+ | [[Category:Class 10]] |
Revision as of 12:13, 3 July 2023
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