Geometry –Triangles: G 5.a; G 5.1, G 5.b; G 5.4; G 6.1,2,3,4

• To assess prior knowledge: have students make circle maps to define the following:– Scalene– Isoceles– Equilateral– Obtuse– Acute– Right

Isocelestriangle

Congruent Triangles

• Teacher would have S’s create Circle map to define Congruent triangles. They could then compare the different maps made (gallery walk – by posting on back wall of room) and decide “what must be on every map” for it to define Congruent triangles.

• A sample map is included. (A Circle map for Similar triangles is also included at end – but intended for a later lesson)

Congruent Triangles

Non-Example Examples

Define Ways to Prove

CPCTC

AASSSS

SASSAS

AAA – similar but NOT congruent

No SSA

A set of points having the same size and shape

1:1 correspondence of equality

Identical

Practice with Correspondence

• The following multi-flow maps are for practice with identifying triangle parts and correspondence

• After identifying relationships, (1/2: event - results) then students can pick out the items that cause congruence with rule – (1/2 : results/causes – event=congruence)

UW = WU

<UTW = <UVW

<UWT = <UWV = 90°

<UTV = <UVT

∆TUV

If

Then

<AASCongruence

If

Then

Sample multi-flow

Ways to Prove Congruent Triangles

SSS SAS ASA

ItemItem Item

AAS

Item

<<Q = <S<P = <RPR = RP

3m = 3m30° = 30 °

Vertical Angles =

NM = OL<NMO = <MOL

MO = OM

JY = CXYB = CHJB = HX

Can use cards with figures printed on them for kids to sort. This is intended as a “working map” that kids will complete.

Congruent Triangles

CombinedFigures

Separated Triangles

Given

.Item<MLN = <LNO

LM = NO

Deductions

LN = NL

90° <PQR = <PQO

QR = OQPQ = PQ..

Congruency Statement

∆MLN = ∆ONLSAS

∆PQR = ∆PQOSAS

PT = RSQT = QS

<RQS = <PQTVertical <

SSAinconclusive

Another example of a working map with S’s filling in blanks for a variety of figures

SAS

ASA

Corresponding sides

are proportion

al

Tilde alone

~

AA

Sizes can differ

Similar ∆

Double Bubble – comparison – similarities & differences

Congruent∆

Corresponding

sides =

Corresponding

angles =

AAS

SSS

Equal & Tilde

Similar Triangles

Non-Example Examples

Define Ways to Prove

AASSSS

SASSAS

A set of points having the same shape

1:1 correspondence of Proportionality of

sides

AAA

Flow Map - Sequencing

Rt. Click or Ctrl click to add

text

Event

Causes Effects

Multi-flow Map– Cause & effect

Brace Map – Whole to part; physical separations

as

Bridge Map – for analogies; always put relating factor

RF:

as