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ACC Math 1

EQ:What does it mean for two triangles to be congruent?

Congruent figures have the same size and same shape.

The parts of congruent triangles that “match” are called corresponding parts.

Two polygons are congruent if ALL pairs of corresponding parts are congruent.

In a congruence statement

ORDER MATTERS!!!! Everything matches up.

NOV DAY

Complete each congruence statement.

CA

E

D

B

F

? ABC DEF

? ACB ECD

C

A

ED

B

Complete each congruence statement.

? GHK GTK

KG

H

T

Complete each congruence statement.

Fill in the blanks

BCA ________ GFE

EGF

CAB

Complete the congruence statement.

_____ JKNMKL

Complete the congruence statement.

_____ CBDABD

EOCT - Warm Up

1) Heather is going to graph y = -3x6 + 3. How is the parent graph transformed?   A) The parent graph is reflected over the x-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.   B) The parent graph is reflected over the y-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.   C) The parent graph is reflected over the y-axis, has a vertical stretch by a factor of 3 and is shifted left 3 units.   D) The parent graph is reflected over the x-axis, has a vertical compression by a factor of 3 and is shifted up 3 units.

Determine the domain of the graphed exponential function.

  A) (-∞, ∞)   B) (-∞, 5]   C) (-∞, 5)   D) (-5, ∞)

Corresponding Parts of Congruent Triangles are

Congruent

Fill in the blanks

If CAT DOG, then A ___

because ________.

O

CPCTCC

A T

O

D

G

Fill in the blanks

If FJH QRS, then ___ and F ___ because _______.Q CPCTC

J H RS

B CPCTCIf XYZ ABC, then ___ and Y ___ because _______.

ZX CA

Complete each congruence statement.

If ABC DEF,

then BC ___EF

Fill in the blanks

If CAT DOG,

then ___ O.A

Fill in the blanks

BAT MON

T ________ ONM_____ MONM ____

N

ATB

BATB

There are 5 ways to prove

triangles congruent.

Side-Side-Side (SSS) Congruence Postulate

All 3 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-Side-Angle (ASA) Congruence Postulate

Two angles and the INCLUDED side

(the side is in between the 2 marked angles)

Angle-Angle-Side (AAS) Congruence Postulate

Two Angles and One Side that is NOT

included

There is one more way to prove triangles congruent, but it’s only for RIGHT TRIANGLES

} Your Only Ways To Prove Triangles Are

Congruent

NO BAD WORDS

There are only 3 types of markings YOU can add to a

triangle if they are not already

marked.

Overlapping sides are congruent in

each triangle by the REFLEXIVE property

Vertical Angles

are congruent

Alt Int Angles are congruent

given parallel

lines

SSS, SAS, ASA, AAS, HL, or not congruent.

SSS

Ex 1

SSS, SAS, ASA, AAS, HL, or not congruent.

AAS

I

Ex 2

Not congruent.

SSS, SAS, ASA, AAS, HL, or not congruent.Ex 3

SSS, SAS, ASA, AAS, HL, or not congruent.Ex 4

SAS

ASA

Ex 5

SSS, SAS, ASA, AAS, HL, or not congruent.

SSS, SAS, ASA, AAS, HL, or not congruent.

Ex 6

SSS

Not congruent

Ex 7

SSS, SAS, ASA, AAS, HL, or not congruent.

SAS

Ex 8

SSS, SAS, ASA, AAS, HL, or not congruent.

SSS, SAS, ASA, AAS, HL, or not congruent.Ex 9

Not congruent.

SSS, SAS, ASA, AAS, HL, or not congruent.

Ex 10

HL

Ex 11

What other pair of angles needs to be marked so that the two triangles are congruent by AAS?

F

D

E

M

L

N

NE

Ex 12

What other pair of angles needs to be marked so that the two triangles are congruent by ASA?

F

D

E

M

L

N

LD

HW – Worksheet both HW – Worksheet both sidessides

5 Ways to proveand

More Congruent Triangles (ws 23)