Congruent triangles – Part 1

CONGRUENT TRIANGLES – PART 1

SLIDESHOW 38, MATHEMATICSMR RICHARD SASAKI, ROOM

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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.

STARTER - ANSWERS

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

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.

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)

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)

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

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)

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

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.