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| # 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. | | # 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 | | # Logical proof of BPT |
| + | # Basic understanding of Trigonometry – ratio of sides in a right triangle |
| + | |
| + | === Pre-requisites === |
| + | |
| + | # Prior knowledge of triangle and prior objects (segment/ray, line, angle) |
| + | # Right triangle – Pythagoras theorem |
| | | |
| === Session plan: === | | === Session plan: === |
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| # Similarity | | # Similarity |
| ## Any circle is similar to any other circle. | | ## Any circle is similar to any other circle. |
− | ## Same holds for Square - <nowiki>https://geogebra.org/m/ceapgrs5</nowiki> | + | ## Same holds for Square - https://geogebra.org/m/ceapgrs5 |
− | ## and Equilateral Triangles and <nowiki>https://geogebra.org/m/kpww6afy</nowiki> | + | ## and Equilateral Triangles and https://geogebra.org/m/kpww6afy |
| ## Quadrilaterals | | ## Quadrilaterals |
| ### Two quadrilaterals of the same number of sides are similar, if | | ### Two quadrilaterals of the same number of sides are similar, if |
| #### (i) their corresponding angles are equal and | | #### (i) their corresponding angles are equal and |
| #### (ii) their corresponding sides are in the same ratio (or proportion) | | #### (ii) their corresponding sides are in the same ratio (or proportion) |
− | ## Triangle - <nowiki>https://geogebra.org/m/mdc43fbt</nowiki> | + | ## Triangle - https://geogebra.org/m/mdc43fbt |
| ### if all angles of one are congruent with the corresponding angles of the second (AAA) | | ### 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) | | ### if the ratio of three corresponding sides are equal (SSS) |
− | # Concept of height of a triangle. <nowiki>https://geogebra.org/m/k56qc3hm</nowiki> | + | # 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) | | ## 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 | | ## 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. | | # 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> | + | ## Draw few triangles and check that this is true – visual proof https://geogebra.org/m/nctk4smk |
− | ## Logical Proof of BPT - <nowiki>https://geogebra.org/m/pjdj65cd</nowiki> | + | ## Logical Proof of BPT - https://geogebra.org/m/pjdj65cd |
| + | |
| + | === Process === |
| + | 1. Congruent and similar triangle - 5. Exploring similarity - changing side lengths and scaling sides.ggb - |
| + | |
| + | 1. Show visual proof of congruence and CPCT. |
| + | |
| + | 2. Show visual proof of similarity and implication for sides (ratio of corresponding sides = and corresponding angles =) |
| + | |
| + | 3. Show for a right angle, if we take another angle, the ratio of opposite side to hypotenuse will be = always, ratio of adjacent angle to hypotenuse and opposite side to adjacent side = always. |
| + | |
| + | 2. 1. Equilateral, Isosceles triangles - Side and angle measure relationships.ggb - Concept of Isosceles triangle – two sides are equal and the two angles opposite these two sides are equal |
| + | |
| + | 3. Shadow cast by sun on stick – arrive at the height of the stick based on length of shadow (angle = 45) |
| + | |
| + | 4. Explain concept of tan, sin and cos |
| + | |
| + | 5. Explain angle of elevation and angle of depression (text book images also) |
| + | |
| + | 6. 3. sin cos tan with sliders for angle and side measures.ggb |
| + | |
| + | 1. Show geogebra file explaining calculation of sin, cos and tan – using slider for angle values. |
| + | |
| + | 2. Show Sin, Cos, Tan values for different angles |
| + | |
| + | 3. Show even if side measure changes, the angles and hence ratios do not change |
| + | |
| + | 7. Show Geogebra file mnemonic file for memorizing formulae for Sin, Cos and Tan |
| + | |
| + | 8. Show workbook to show the pattern to memorize sin, cos, tan of common angles |
| | | |
− | === Assessment: === | + | === Evaluation: === |
| + | Slides for rapid questions, with images |
| [[Category:Triangles]] | | [[Category:Triangles]] |
| [[Category:Class 10]] | | [[Category:Class 10]] |