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