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