Download Chapter 4 - Mater Academy Charter Middle/ High

CHAPTER 4
CONGRUENT TRIANGLES
4.1 CONGRUENT FIGURES
4.2 TRIANGLE CONGRUENCE BY SSS AND SAS
4.3 TRIANGLE CONGRUENCE BY ASA AND AAS
• STUDENTS WILL BE ABLE TO
• RECOGNIZE CONGRUENT FIGURES AND THEIR CORRESPONDING PARTS
• PROVE TWO TRIANGLES ARE CONGRUENT USING SSS AND SAS
• PROVE TWO TRIANGLES ARE CONGRUENT USING ASA AND AAS
MA.912.G.4.4 ANDMA.912.G.4.5 AND MA.912.G.4.5
MA.912.D.6.4 AND MA.912.G.8.5
NOTES FOR 4.1-4.3
• IN ORDER TO PROVE THAT TWO FIGURES ARE CONGRUENT WE NEED TO
MAKE SURE THAT ALL SIDES AND ALL ANGLES OF ONE POLYGON ARE
EQUAL TO ALL ANGLES AND SIDES OF ANOTHER POLYGON.
• IN ORDER TO DO THIS, WE MUST FIRST BE ABLE TO DECIDE WHICH SIDES
AND ANGLES ON ONE POLYGON MATCH WITH THE SIDES AND ANGLES
OF ANOTHER POLYGON… WE CALL THESE MATCHING PIECES
“CORRESPONDING PARTS”.
• IF THE POLYGONS ARE CONGRUENT THEN THE CORRESPONDING PARTS
SHOULD BE EQUAL.
NOTES FOR 4.1-4.3
• PROVING TWO POLYGONS ARE CONGRUENT COULD TAKE A LOT OF
WORK. FOR EXAMPLE IF WE WANT TO SHOW THAT TWO TRIANGLES
ARE CONGRUENT WE WOULD NEED TO SHOW THAT ALL 3 ANGLES
AND ALL 3 SIDES OF ONE TRIANGLE ARE EQUAL TO ALL 3 ANGLES
AND ALL 3 SIDES OF ANOTHER TRIANGLE! THIS IS 6 DIFFERENT PAIRS
OF CONGRUENT PARTS!!!
• WE CAN USE LOGIC AND A FEW THEOREMS TO MAKE SOME SHORT
CUTS.
NOTES FOR 4.1-4.3
• THEOREM: 3RD ANGLES THEOREM: IF TWO ANGLES OF ONE TRIANGLE ARE
CONGRUENT TO TWO ANGLES OF ANOTHER TRIANGLE THEN THE 3RD
ANGLES OF BOTH MUST BE CONGRUENT.
• SSS THEOREM: IF 3 SIDES OF ONE TRIANGLE ARE CONGRUENT TO 3 SIDES
OF ANOTHER TRIANGLE THEN THE TRIANGLES ARE CONGRUENT
• SAS THEOREM: IF 2 SIDES OF ONE TRIANGLE AND THE INCLUDED ANGLE
OF THE TRIANGLE ARE CONGRUENT TO 2 SIDES AND THE INCLUDED
ANGLE OF ANOTHER TRIANGLE THEN THE TWO TRIANGLES ARE
CONGRUENT
NOTES FOR 4.1-4.3
• ASA THEOREM: IF 2 ANGLES OF ONE TRIANGLE AND THE INCLUDED SIDE
OF THE TRIANGLE ARE CONGRUENT TO 2 ANGLES AND THE INCLUDED
SIDE OF ANOTHER TRIANGLE THEN THE TWO TRIANGLES ARE
CONGRUENT
• AAS THEOREM: IF 2 ANGLES AND 1 SIDE OF ONE TRIANGLE ARE
CONGRUENT TO 2 ANGLES AND 1 SIDE OF ANOTHER TRIANGLE THEN THE
TRIANGLES ARE CONGRUENT
• HYPOTENUSE LEG THEOREM: IF TWO RIGHT TRIANGLES HAVE
CONGRUENT HYPOTENUSES AND ANOTHER PAIR OF EQUAL SIDES THEN
THE TWO TRIANGLES ARE CONGRUENT
CLASSWORK/HOME LEARNING
• PAGE 222 #10-19, 35, 36, 39, 40, 41
• PAGE 231 #11-14, 17, 24-26, 35-38
• PAGE 238 #13, 16-18, 25, 32-35
4.4: CORRESPONDING PARTS OF CONGRUENT TRIANGLES
ARE CONGRUENT
4.5: ISOSCELES AND EQUILATERAL TRIANGLES
• STUDENTS WILL BE ABLE TO:
• USE TRIANGLE CONGRUENCE AND CPCTS TO PROVE THAT PARTS OF
TWO TRIANGLES ARE CONGRUENT
• USE AND APPLY THE PROPERTIES OF ISOSCELES AND EQUILATERAL
TRIANGLES
MA.912.G.4.4 ANDMA.912.G.4.5 AND MA.912.G.4.5
MA.912.D.6.4 AND MA.912.G.8.5
NOTES FOR 4.4 AND 4.5
• ONCE YOU KNOW THAT TWO TRIANGLES ARE CONGRUENT BASED ON
SSS, SAS, ASA, AAS AND HL YOU CAN NOW MAKE CONCLUSIONS
ABOUT SPECIFIC CORRESPONDING PARTS OF TRIANGLES.
• IF YOU KNOW THAT TWO SHAPES ARE EXACTLY THE SAME SIZE AND
EXACTLY THE SAME SHAPE (IE: THEY ARE CONGRUENT) THEN IT MAKES
SENSE THAT SPECIFIC ANGLES AND SPECIFIC SIDES THAT ARE
CORRESPONDING SHOULD BE THE SAME TOO… THIS IS WHAT CPCTC
MEANS.
NOTES FOR 4.4 AND 4.5
• WITH ISOSCELES AND EQUILATERAL TRIANGLES WE KNOW EVEN MORE
INFORMATION BECAUSE WE KNOW THAT SIDES ARE ACROSS FROM
EQUAL ANGLES
• THIS MEANS THAT IN AN ISOSCELES TRIANGLE WE HAVE 2 EQUAL SIDES
AND THE TWO ANGLES ACROSS FROM THEM ARE ALSO EQUAL.
• IN AN EQUILATERAL TRIANGLE, ALL SIDES AND ALL ANGELS ARE EQUAL
AND ALL ANGLES MEASURE 60 DEGREES.
CLASSWORK/HOMEWORK
• PAGE 247 #6, 11-13, 23-26
• PAGE 254 #6-9, 16-19, 37-40
4.6: CONGRUENCE IN RIGHT TRIANGLES
4.7: CONGRUENCE IN OVERLAPPING TRIANGLES
• STUDENTS WILL BE ABLE TO
• PROVE RIGHT TRIANGLES ARE CONGRUENT USING THE HYPOTENUSE
LEG THEOREM
• IDENTIFY CONGRUENT OVERLAPPING TRIANGLES AND USE CONGRUENT
TRIANGLE THEOREMS TO PROVE TRIANGLES ARE CONGRUENT.
MA.912.G.4.4 ANDMA.912.G.4.5 AND MA.912.G.4.5
MA.912.D.6.4 AND MA.912.G.8.5
NOTES FOR 4.6 AND 4.7
• HYPOTENUSE LEG THEOREM: IF TWO RIGHT TRIANGLES HAVE
CONGRUENT HYPOTENUSES AND ANOTHER PAIR OF EQUAL SIDES THEN
THE TWO TRIANGLES ARE CONGRUENT
• WHEN FIGURES ARE OVERLAPPED IT MAY BE USEFUL TO SEPARATE THE
FIGURES AND IDENTIFY THE SHARED PARTS
CLASSWORK / HOME LEARNING
•PAGE 262# 15, 29-31
•PAGE 268# 8-13, 17, 29-32
OFFICE AID
I AM AT A MEETING IN THE MAIN OFFICE… HERE’S YOUR LIST OF
THINGS TO DO:
1.
COME AND SEE ME IN THE OFFICE FIRST!!!!
2.
AT THE BACK OF THE ROOM THERE IS A HOLE PUNCHER AND
PAPERS – PLEASE HOLE PUNCH
3.
CLEAN UP MY CLASSROOM
4.
THE BASKETS IN THE BACK HAVE PAPERS AND FOLDERS PLEASE PUT
THE PAPERS INTO THE CORRECT STUDENT FOLDERS. IF THE STUDENT
HAS NO FOLDER, JUST LEAVE OUT.