Monday, September 7, 2015MAT 145. Monday, September 7, 2015MAT 145.
Monday, September 23 rd
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Transcript of Monday, September 23 rd
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Monday, September 23rd
S is the centroid. 1. If NP=7, what is PL?2. If SQ=4, what is SN?
Warm Up
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Week at a Glance
Monday: Review-Centroid and Proofs Tuesday: parallelogram proofs Wednesday: Similar Triangles Thursday: Similarity Triangle Proofs Friday: Similiarity Triangle Proofs CW
Test #2-Next Wednesday
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Part 1: Centroids
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A median of a triangle is a segment whose endpoints are a vertex of the
triangle and the midpoint of the opposite side.
Every triangle has three medians, and the medians are concurrent.
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The point of concurrency of the medians of a triangle is the centroid of the triangle . The
centroid is always inside the triangle.
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Vertex vs. Mid-Segment 1. Vertex to Centroid = 2/3 distance
of the median
2. Mid-segment to centroid=1/3 distance of median
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Median C
entr
oid
Vert
ex
mid
segm
ent
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In ∆LMN, RL = 21. Find LS.
LS = 14
Centroid Thm.
Substitute 21 for RL.
Simplify.
#1
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In ∆LMN, SQ =4. Find NQ.
SQ= mid-segment to centroid
#2
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Median C
entr
oid
Vert
ex
mid
segm
ent
444
Total: 4 + 4 + 4 = 12
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Algebra Midsegment to centroid= 1/3 distance
4=1/3NQ*Use division (multiply by reciprocal)
1213
14
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In ∆JKL, ZW =8 find ZK
ZW=midsegment to centroid
#3
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Median C
entr
oid
Vert
ex
mid
segm
ent
888
Total: 8 + 8 =16
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In ∆JKL, LX = 8.1. Find LZ.
Centroid Thm.
Substitute 8.1 for LX.
Simplify.LZ = 5.4
#4
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You Try! Z is the centroid. YZ = 5, JX= 10, KW = 15
1.KX2.ZJ3.YJ4.KZ
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Part 2: Proofs
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2 markings you can add if they aren’t marked
already
Don’t Forget!
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Share a sideReason: reflexive
property
Vertical AnglesReason: Vertical Angles are congruent
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In a congruence statement
ORDER MATTERS!!!! Everything matches up.
AUG DAY
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1. Angles are written with either 1 letter or three letters!
2. Sides are written with two letters
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1. Write down two congruent sides
2. Write two congruent angles
3. GAU is congruent to _________
AUG DAY
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There are 5 ways to prove
triangles congruent.
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Remember • Go around clockwise
• Can’t skip sides and angles
BP
O
E D
U
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Side-Side-Side (SSS) Congruence Postulate
All Three sides in one triangle are congruent to all
three sides in the other triangle
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Side-Angle-Side (SAS) Congruence Postulate
Two sides and the INCLUDED angle
(the angle is in between the 2 marked sides)
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Angle-Angle-Side (AAS) Congruence Postulate
Two Angles and One Side that is NOT
included
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Angle-Side-Angle (ASA) Congruence Postulate
Two angles and the INCLUDED side(the side is in between the 2 marked
angles)
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There is one more way to prove triangles congruent, but it’s only for RIGHT TRIANGLES…Hypotenuse Leg
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The ONLY Ways To Prove
Triangles Are Congruent
NO BAD WORDS
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Key Tips • First statement is always GIVEN. • Other statements may also be
GIVEN • Last statement should be what you
are trying to prove and be using one of our 5 triangle Postulates (SSS, ASA, Etc.)
• Draw in your dashes and angles • Try to remember all the
rules/theorems/postulates we have covered since the beginning of the year!
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CW- More Practice with Proofs
1-9
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HW: Proof Scramble