congruent triangles – part 1
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Congruent triangles – Part 1. Slideshow 38, Mathematics Mr Richard Sasaki, Room 307. Starter. Please answer the questions on the worksheet provided. You will need protractors, you may use your own or borrow one. Starter - Answers. Starter - Answers. Starter - Answers. Starter - Answers. - PowerPoint PPT PresentationTRANSCRIPT
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CONGRUENT TRIANGLES – PART 1
SLIDESHOW 38, MATHEMATICSMR RICHARD SASAKI, ROOM
307
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STARTER
PLEASE ANSWER THE QUESTIONS ON THE WORKSHEET PROVIDED. YOU WILL NEED PROTRACTORS, YOU MAY USE YOUR OWN OR BORROW ONE.
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STARTER - ANSWERS
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STARTER - ANSWERS
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STARTER - ANSWERS
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STARTER - ANSWERS
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STARTER - ANSWERS
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STARTER - ANSWERS
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OBJECTIVES
• UNDERSTAND THE WAYS AND NAMES OF WAYS THAT WE CAN TEST IF TWO TRIANGLES ARE CONGRUENT• USE THESE RULES TO STATE WHETHER
TRIANGLES ARE CONGRUENT AND FIND MISSING ANGLES
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CONGRUENT TRIANGLES
WHEN TWO TRIANGLES ARE THE SAME SIZE AND SHAPE, THEY ARE CONGRUENT.
IF WE HAVE INFORMATION THAT PRODUCES A UNIQUE TRIANGLE, WE CAN CHECK TO SEE IF IT IS CONGRUENT TO ANOTHER.
CHECK THE TWO WORKSHEETS FROM THE LAST TWO LESSONS.
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DRAWING UNIQUE TRIANGLES
THE MINIMUM AMOUNT OF INFORMATION NEEDED IS EITHER:
•THREE EDGES•ONE EDGE AND TWO ANGLES•TWO EDGES AND ONE ANGLE
(IN SPECIAL CASES)
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CONGRUENT TRIANGLES
WITH THIS INFORMATION WE CAN CHECK WHETHER TWO TRIANGLES ARE CONGRUENT:
THREE EDGES
5cm 4cm
2cm
5cm 4cm
2cm
(SSS) ONE EDGE AND TWO ANGLES
4cm 4cm
80o60o80o60o
(AAcorS)
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ONE EDGE AND TWO ANGLES
4cm 4cm
80o60o80o60o
(AAcorS)
AAcorS?THIS MEANS “TWO ANGLES AND A CORRESPONDING SIDE”.THE ANGLES MUST BE IN THE SAME PLACE IN RELATION TO THE SIDE.
NOTE: THESE ARE NOT CONGRUENT…
4cm 4cm
80o
60o
80o60o
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CONGRUENT TRIANGLES
WITH THIS INFORMATION WE CAN CHECK WHETHER TWO TRIANGLES ARE CONGRUENT:
TWO EDGES WITH AN ANGLE BETWEEN THEM
5cm 4cm40o5cm 4cm40o
(SAS)THE HYPOTENUSE AND ANY OTHER CORRESPONDING SIDE
5cm 5cm
3cm3cm(RHS)
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RHS?RHS MEANS “RIGHT HYPOTENUSE SIDE” BUT REALLY THIS RULE WORKS FOR ANY TWO SIDES ON A RIGHT-ANGLED TRIANGLE.
THE HYPOTENUSE AND ANY OTHER SIDE
5cm 5cm
3cm3cm(RHS)
NOTE: HYPOTENUSE IS THE LONGEST EDGE.
NOTE: THESE ARE ALSO CONGRUENT BY SAS.
4cm 4cm
3cm3cm
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ANSWERS
b. SSS2. yes, no, yes, no, yes3. ∆ABC ≅ ∆YXZ by SAS as AB=YX, BC=XZ and ABC = YXZ.4. ∆ABC ≅ ∆XZY by RHS as AB = XZ, BC = YZ and ACB = XYZ which are both right-anglesb. 5. The two angles and edge are the same size but don’t correspond.