WarmupSolve for x in the picture below:

3x+22

5x-4

Section 4.1: Congruent Figures

LEQ: What are congruent figures and their properties?

Pop Quiz write on your note sheetWrite never, sometimes or always.1.An acute triangle is ____ congruent to an obtuse

triangle.2.A polygon is ____ congruent to itself.3.A right triangle is _____ congruent to another

right triangle.4.If ∆ABC ≅ ∆XYZ, ∠A is ____ congruent to ∠Y.5.If ∆ABC ≅ ∆XYZ, ∠B is ____ congruent to ∠Y.

What are congruent polygons? What are their propertiesTalk it over with a partner (no need to write,

just brainstorm)

Slides, flips, and turnsCongruent figures have the same size and shape.

When two figures are congruent, they can be moved so that they fit exactly on top of each other. Examples of movements:

Slides

Flips

Turns

Congruent PolygonsCongruent polygons have congruent

corresponding parts aka matching sides and angles. Sides and angles must match up after flipped,

turned, or slid. Order is critical!!

Name the corresponding sides and angles

<A corresponds to <B corresponds to<C corresponds to

A

B C D

E

F

<E

<F

<D

AC

BC

AB

ED

FD

EF

corresponds tocorresponds tocorresponds to

If ABCDE FGHIJ…Corresponding angles/sides are congruent.

Order matters in congruency statement.

Ex. <A <F <D <I

CD HI AE FJ

FA

G

B

H

C

ID

J

E

Congruent Triangles3 pairs of congruent angles3 pairs of congruent sides

Congruency statement: ABC EGR

A

E

R

CB

G

*Applications to ProofsWhen the definition of congruent triangles is used in a proof we write,

Corr. parts of Δ’s are

or CPCTC !!!

Examples of CPCTCIf ΔEFG ΔRTW, and this is used in a proof before the

last step (meaning we need to use this fact to make other conclusions), then any conclusions we make based off of this congruency statement has the reason “corresponding parts of congruent triangles are congruent or CPCTC”

Closure to 4.1Go back to pop quiz1.An acute triangle is ____ congruent to an obtuse

triangle.2.A polygon is ____ congruent to itself.3.A right triangle is _____ congruent to another

right triangle.4.If ∆ABC ≅ ∆XYZ, ∠A is ____ congruent to ∠Y.5.If ∆ABC ≅ ∆XYZ, ∠B is ____ congruent to ∠Y.

Hwk: p. 200-2021-12, 30-35, 38-40