DEFINING CONGRUENCE

Investigation 2.1 and 2.2

4 3 2 1 0In addition to 3, student is able to teach others how to apply properties of transformations.

Apply properties of transformations to perform and explain sequences of transformations and prove figures are congruent.   

Apply properties of transformations to perform sequences of transformation.

With help, apply properties of transformations to perform sequences of transformation.

Even with help, I am unable to apply properties of transformations.

Learning Goal 2(8.G.A.2, 8.G.A.3):Apply properties of transformations to perform and explain sequences of transformations and prove figures are congruent.

Congruent

• Tell your partner what you think congruent means.

• Two figures have the same size and same shape are congruent.

• Draw an example of objects that are congruent.

Connecting Congruent Polygons When two polygons are congruent, you

can match vertices in a way that pairs sides and angles of the same size.

Quadrilaterals ABCD and RSPQ are congruent.

What are pairs of congruent sides?

What are pairs ofcongruent angles?

Connecting Congruent Polygons How can you flip, turn, and or

slide one quadrilateral onto the other?

Write down which vertices inquadrilateral ABCD correspondto which vertices in quadrilateral PQRS.The arrow “→” means “corresponds to.”

A → B → C → D →

R S

P Q

Geometric Notation

AB means “line segment AB” The symbol means “is

congruent to.” Complete these statements to

show which pairs of sides in thetwo quadrilaterals are congruent.

AB BC CD DA

SR

PS

RQ

PQ

Geometric Notation

The notation A means “angle A.” Complete these statements

to show which angles arecongruent.

A B C D

RSPQ

Geometric Notation

Triangle ABC and RQP show a common way of marking congruent sides and angles.

The sides with the same number of tic marks are congruent.

The angles with the same number of arcs are congruent.

Geometric Notation

Copy the two figures.

ΔABC ΔZYX Use tic marks and

arcs to show which sides and angles are congruent to each other.