Download Triangle Hints

Triangle Properties
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Notes
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Hwk Hints (Week of 10/26):
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Angle Sum Theorem: sum of measure of angles of triangle are 180
Exterior Angle Theorem: exterior angle = sum of 2 remote interior angles.
No Choice/3rd Angle Theorem: if 2 angles of 1 triangle are congruent ot 2 angles of another triangle,
then 3rd angles are congruent
SG 4-2 WS:
 pg 189 #2 - angles Q and R are congruent
 pg 190 #4: angle 3 = 35 + 36, angle 1 = angle 2 + 80
Skills 4-2 WS (Honors/Magnet)
 #2: (180-146)/2
Skills 5-2 WS:
 #1-4: Remember if the 3 angles are given, the exterior angle is always the largest one.
 #5-6, looking for all of its remote interior angles
 #7-8: looking for all of its exterior angles.
 #9-12: compare the associated side values to determine the angle relationships (>, < or =)
 #13-16: compare the associated angle values to determine side relationships (>, < or =)
pg263 (Book Assignment)
 #13: x + x > 10; x > 5
 #52: 7 + 12 > x; 19 > x
Skills 5-4 WS (Honors/Magnet)
 #17-20: use distance formula to find all of the sides and then check if 2 smaller sides are greater
than the larger side.
SG4-1 WS
 Pg184 #8: set 4y=3y+2 to solve for y.
 Pg184 #9: use distance formula to find the sides then compare to see what type of triangle it is
Pg144 (Book assignment – Honors/Magnet)
 #11: need to set 10=2x-8 because others either give negative side or perimeter > 45.
Quiz Hints (Week of 10/26):
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Triangle Properties:
 Be able to find the range of the 3rd side of a triangle
 Be able to determine whether or not 3 sides are a triangle
 Be able to solve for a missing angle of a triangle
 Be able to classify a triangle based on sides and/or angles.
 Know the relationship between exterior angles and remote interior angles.
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Triangles
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Notes
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Classification of Triangles
 Based on angles: acute, obtuse, right, equiangular
 Based on sides: scalene, isosceles, equilateral
Transformations
 Reflect/flip over x-axis: y-coordinate changes signs
 Reflect/flip over y-axis: x-coordinate changes signs
 Slide: when moving right/left then add/subtract from x-coordinate, when moving up/down then
add/subtract from the y-coordinate
ICA (Week of 11/2)
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Conclusions -Triangles WS
 #1: identify all SSE, SSI, corr, alt int, alt ext
 #2: think about all of the relationships between the various angles
 #3: identify the type of triangle based on angles & sides. Also find the missing angles.
 #4-7: think about types of triangles based on angles and sides
T-P-S Triangle Proofs WS
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Homework (Week of 11/2)
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 #1: must show that no sides are congruent
 #2: must show that all angles are less than 90
 #3: remember all radii are congruent
Skills 4-3 WS
 #7: Translation/Slide (x+6,y+2)
 #8: Reflection over y-axis (change in x-coordinate)
RT - Proving Triangles Congruent (ASA/AAS)
 #9: step 5: angles R and U congruent, reason 5: if || then alt int congruent
Triangle Proofs WS
 #1: in order to prove triangle RPM is an obtuse triangle, you must prove that 1 of the angles is
obtuse
 #2: remember, all radii are congruent
 #3: remember if 2 lines are perpendicular, they form a right angle
pg 195 (book)
 #7: Since x-coordinates change, reflect over y-axis
 #24: Since all x-coordinates moved 7 to right, translation/slide
 #25: Rotate
Congruent Triangle/Transformation WS
 #1 Reflexive Property
 #3: Vertical Angles
Proving Triangles Congruent WS #1
 #2: use the fact that if perpendicular, then right angle is formed
 #3: Step 4: SI congruent to NL (Addition Property)
Pg120 (Honors/Magnet)
 #3, 4, 7 - done in 4 steps
 #5,15 – done in 5 steps
 #6,8,11, 12 – done in 6 steps
 #8 & 15: use the Addition Property
Quiz Hints (Week of 11/2):
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Triangles Quiz #2:
 Matching (most vocab from triangle properties notes)
 1 question on Transforming a triangle
 Be sure to look over #2 from Triangle Proofs WS
 Review HOT/CAT proofs on page 3-4 of notes. One of them is on the quiz
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ICA (Week of 11/9)
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Pg135 (Honors/Magnet)
 #2: 6 steps
 #4: 7 steps, need to show CD = DE before you can say median
 #5: 3 steps, use the fact of if sides then angles
 #8: 6 steps, will use Addition Property
SG4-6 WS
 pg213 #7: 4 steps
 pg214 #7: 6 steps (using CPCTC)
Coordinate WS
 When finding median, need to use midpoint formula.
 When trying to determine if 2 segments form right angles, find slopes. If opposite reciprocals
then you have right angle.
 When determining if parallel, slopes must be the same.
Homework (Week of 11/9)
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Proving Triangles Congruent WS #2
 #1: use the fact that if perpendicular, then right angle is formed
 #5: steps 1-4: given
 #1, 4 and 5 dealing with Right triangles. Will use HL, HA, LA or LL as reason for triangles
being congruent.
 Hint: When triangles share a common side, use reflexive property.
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CPCTC WS
 #4 & #5: use the fact that all radii are congruent
 #6: Use reflexive twice. Need to prove 2 pairs of triangles are congruent.
Overlapping Triangle WS (Honors/Magnet)
 #6: Will use CPCTC
pg219 (book - Regular)
 #30: 9steps. Must 1st prove triangles are congruent, then use CPCTC, Right Angle Theorem and
finally definition of perpendicular
Pg152 (book – Magnet/Honors)
 #1: 5 steps; don’t forget supplements of congruent angles are congruent
 #2: 5 steps; need to prove triangles are congruent first
 #4: 6 steps; don’t forget complements of congruent angles are congruent
 #5: 4 steps
 #6: 7 steps; use reflexive, CPCTC
Quiz Hints (Week of 11/9):
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3 proofs. Be sure to review all proofs from homework and notes.
Be able to identify medians and altitudes.
Be able to identify different methods for solving triangles.
Be able to solve for angles or sides of an isosceles triangle.
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ICA (Week of 11/16)
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Homework (Week of 11/16)
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Coordinate WS
 When finding median, need to use midpoint formula.
 When trying to determine if 2 segments form right angles, find slopes. If opposite reciprocals
then you have right angle.
 When determining if parallel, slopes must be the same.
YTMT – Indirect Proofs
 #1: need to show perpendicular bisector
 #4: if altitude, then angles 1 and 2 are right angles and congruent.
Scavenger Hunt: Triangle Vocabulary
 #1 vertex angle
Puzzle Game: Triangle Review
 #5: Assume JH is congruent to JK.
 #6: use pythagorean theorem to determine type of triangle
Equidistance WS
 #3: Using both TPEEEDPB and POPBTEE
Indirect Proofs WS
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Always start with proof statement and its opposite. Assume its opposite is true. Using
paragraph proof show a contradiction causing assumption to be false and conclude the proof
statement is true
Exam Hints (Week of 11/16):
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