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1 MEDIANS ARE PROPORTIONAL ALTITUDES ARE PROPORTIONAL ANGLE BISECTORS ARE PROPORTIONAL PERIMETERS ARE PROPORTIONAL ANGLE BISECTORS FORM PROPOR. SEG. PROBLEM.

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Presentation on theme: "1 MEDIANS ARE PROPORTIONAL ALTITUDES ARE PROPORTIONAL ANGLE BISECTORS ARE PROPORTIONAL PERIMETERS ARE PROPORTIONAL ANGLE BISECTORS FORM PROPOR. SEG. PROBLEM."— Presentation transcript:

1 1 MEDIANS ARE PROPORTIONAL ALTITUDES ARE PROPORTIONAL ANGLE BISECTORS ARE PROPORTIONAL PERIMETERS ARE PROPORTIONAL ANGLE BISECTORS FORM PROPOR. SEG. PROBLEM 6 PROBLEM 7 PROBLEM 8 PROBLEM 9 STANDARDS 4 and 5 END SHOW SPECIAL SEGMENTS IN A TRIANGLE PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

2 2 Standard 4: Students prove basic theorems involving congruence and similarity. Los estudiantes prueban teoremas básicos que involucran congruencia y semejanza. Standard 5: Students prove triangles are congruent or similar and are able to use the concept of corresponding parts of congruent triangles. Los estudiantes prueban que triángulos son congruentes o semejantes y son capaces de usar el concepto de partes correspondientes de triángulos congruentes. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

3 3 STANDARDS 4 and 5 ALTITUDE: A segment from a vertex of a triangle perpendicular to the line containing the opposite side. ALTURA: Un segmento desde el vértice de un triángulo perpendicular a la línea conteniendo el lado opuesto. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

4 4 STANDARDS 4 and 5 PERPENDICULAR BISECTOR: A line or segment that passes through the midpoint of a side of a triangle and is perpendicular to that side.. BISECTRIZ PERPENDICULAR: Una línea o segmento que pasa a través del punto medio de un lado de un triángulo y es perpendicular a ese lado. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

5 5 STANDARDS 4 and 5 MEDIAN: A segment that connects a vertex of a triangle to the midpoint of the opposite side. MEDIANA: Un segmento que conecta un vertice de un triángulo a el punto medio del lado opuesto. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

6 6 STANDARDS 4 and 5 ANGLE BISECTOR: A segment from a vertex to the opposite side that bisects (divides in two equal parts) the angle of the triangle. BISECTRIZ ANGULAR: Un segmento desde un vértice a el lado opuesto que biseca (divide en dos partes iguales) el ángulo de el triángulo. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

7 7 STANDARDS 4 and 5 Draw an isosceles triangle and draw an altitude, a perpendicular bisector, a median and an angle bisector from the vertex angle. What do you observe? Altitude PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

8 8 STANDARDS 4 and 5 Draw an isosceles triangle and draw an altitude, a perpendicular bisector, a median and an angle bisector from the vertex angle. What do you observe? Perpendicualr Bisector PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

9 9 STANDARDS 4 and 5 Draw an isosceles triangle and draw an altitude, a perpendicular bisector, a median and an angle bisector from the vertex angle. What do you observe? Median PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

10 10 STANDARDS 4 and 5 Draw an isosceles triangle and draw an altitude, a perpendicular bisector, a median and an angle bisector from the vertex angle. What do you observe? Angle Bisector PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

11 11 STANDARDS 4 and 5 Draw an isosceles triangle and draw an altitude, a perpendicular bisector, a median and an angle bisector from the vertex angle. What do you observe? Altitude Perpendicualr Bisector Median Angle Bisector Lets put them all together So, all of them occupy the same Geometric Space in the triangle! Could you do something similar with an equilateral triangle in all the vertices? PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

12 12 A B C K L M KL AB MK CA LM BC STANDARDS 4 and 5 CABMKL KL AB MK CA LM BC OR REVIEW: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

13 13 A B C K L M AB KL CA MK BC LM N KN D AD In simlar triangles MEDIANS are proportional to sides: STANDARDS 4 and 5 KL AB MK CA LM BC KN AD OR PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

14 14 J I K S J U T R TU IK STANDARDS 4 and 5 = JS = IJK TJU, R is the midpoint of TU and S is the midpoint of IK. TU= 10, JR= 6, IK = 30. Find JS. S R J U T I K JS JR (6) = (30)(6) 10 JS = JS JS=18 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

15 15 A B C K L M In similar triangles ALTITUDES are proportional to sides: AB KL CA MK BC LM O KO E AE STANDARDS 4 and 5 KL AB MK CA LM BC KO AE OR PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

16 16 F AF P KP A B C K L M In similar triangles ANGLE BISECTORS are proportional to sides: AB KL CA MK BC LM STANDARDS 4 and 5 KL AB MK CA LM BC KP AF OR PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

17 17 JR JS JT JT+TI STANDARDS 4 and 5 S R J U T I K J I K S J U T R JS is an angle bisector. If TJ = 14, IT=22, and JS= 30, what is the value for JR? Suppose IJK TJU = JR = (30) = (14)(30) 36 JR = JR 30 JR = PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

18 18 A B C K L M AB KL CA MK BC LM In similar triangles PERIMETERS proportional to sides: KL MK LM++ ABCA BC ++ STANDARDS 4 and 5 KL AB MK CA LM BC KLMKLM++ AB CA BC++ OR PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

19 19 JK JU JT+JU+TU PERIMETER IJK STANDARDS 4 and 5 S R J U T I K Given: JT=20, JU=30, TU=70, AND JK=90, what is the perimeter of IJK? Suppose TJU IJK. J I K S J U T R = PERIMETER IJK = 120 PERIMETER IJK = 3 (120) PERIMETER IJK = PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

20 20 A B C D AB AC DC BD STANDARDS 4 and 5 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

21 21 IS SK JI JK STANDARDS 4 and 5 S R J U T I K JS is an angle bisector. JI= X+5, JK=X+3, IS=3, and SK=2. Find the value for X. Suppose IJK TJU. = = 3(X+3) = 2(X+5) 3X + 9 = 2X X = 2X X X = 1 X+5 X X PRESENTATION CREATED BY SIMON PEREZ. All rights reserved


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