Download - Monday, September 23 rd
Monday, September 23rd
S is the centroid. 1. If NP=7, what is PL?2. If SQ=4, what is SN?
Warm Up
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
Part 1: Centroids
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.
The point of concurrency of the medians of a triangle is the centroid of the triangle . The
centroid is always inside the triangle.
Vertex vs. Mid-Segment 1. Vertex to Centroid = 2/3 distance
of the median
2. Mid-segment to centroid=1/3 distance of median
Median C
entr
oid
Vert
ex
mid
segm
ent
In ∆LMN, RL = 21. Find LS.
LS = 14
Centroid Thm.
Substitute 21 for RL.
Simplify.
#1
In ∆LMN, SQ =4. Find NQ.
SQ= mid-segment to centroid
#2
Median C
entr
oid
Vert
ex
mid
segm
ent
444
Total: 4 + 4 + 4 = 12
Algebra Midsegment to centroid= 1/3 distance
4=1/3NQ*Use division (multiply by reciprocal)
1213
14
In ∆JKL, ZW =8 find ZK
ZW=midsegment to centroid
#3
Median C
entr
oid
Vert
ex
mid
segm
ent
888
Total: 8 + 8 =16
In ∆JKL, LX = 8.1. Find LZ.
Centroid Thm.
Substitute 8.1 for LX.
Simplify.LZ = 5.4
#4
You Try! Z is the centroid. YZ = 5, JX= 10, KW = 15
1.KX2.ZJ3.YJ4.KZ
Part 2: Proofs
2 markings you can add if they aren’t marked
already
Don’t Forget!
Share a sideReason: reflexive
property
Vertical AnglesReason: Vertical Angles are congruent
In a congruence statement
ORDER MATTERS!!!! Everything matches up.
AUG DAY
1. Angles are written with either 1 letter or three letters!
2. Sides are written with two letters
1. Write down two congruent sides
2. Write two congruent angles
3. GAU is congruent to _________
AUG DAY
There are 5 ways to prove
triangles congruent.
Remember • Go around clockwise
• Can’t skip sides and angles
BP
O
E D
U
Side-Side-Side (SSS) Congruence Postulate
All Three sides in one triangle are congruent to all
three sides in the other triangle
Side-Angle-Side (SAS) Congruence Postulate
Two sides and the INCLUDED angle
(the angle is in between the 2 marked sides)
Angle-Angle-Side (AAS) Congruence Postulate
Two Angles and One Side that is NOT
included
Angle-Side-Angle (ASA) Congruence Postulate
Two angles and the INCLUDED side(the side is in between the 2 marked
angles)
There is one more way to prove triangles congruent, but it’s only for RIGHT TRIANGLES…Hypotenuse Leg
The ONLY Ways To Prove
Triangles Are Congruent
NO BAD WORDS
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!
CW- More Practice with Proofs
1-9
HW: Proof Scramble