Download Course: 7th Grade Math DETAIL LESSON PLAN Thursday, January

Course: 7th Grade Math
Student Objective
(Obj. 3c)
TSW… identify and justify the congruency of two figures.
Lesson
7-5 Congruent Figures
DETAIL LESSON PLAN
Thursday, January 12 / Friday, January 13
Textbook Pages: 346-349
Homework
Congruent Figures WS (Berg created)
Last Night’s Homework
Review for Transformation Quiz
Bellwork
Transformation quiz
Prior Knowledge
 Review answers to bellwork quiz on transformations.
 LAST WEEK, we started our unit on Geometry. We learned how to transform different types of geometric figures.
Anticipatory Set
 TODAY, we will continue talking about geometry. We will learn to identify geometric figures that are CONGRUENT!

What are “Congruent Figures”
Why do we need to learn about Congruent Figures?
Where do we see Congruent Figures?
Well…. Let’s see…..

Show PowerPoint
We see congruent figures in Architecture.
The U.S. Dept. of Treasury uses congruency when it makes money!
Manufactures use congruency when they make their products.
Teacher Input
 Review the answers to the bellwork quiz.
 Pass out student notes.
 Use PowerPoint “Congruent Figures Seen In the Real World” to lead into today’s lesson on congruent figures.
 Define and give example of congruent figures. (circle map)
 Explain and demonstrate how to match-up corresponding angles and sides using arcs and tick marks.
 Explain and demonstrate how to name corresponding figures.
 Allow students to work the “you try” problems.
 Classwork: Worksheet – Congruent Figures Problem #’s 1-5 (Berg created) (Think, Pair, Share)
Extra Practice: Above worksheet problem #’s 6-9?
Homework: Congruent Figures WS (Berg created)
Assessment
Question students for understanding. Observation students as they work on their classwork.
Closure
 Can anyone give me an example of where you would see congruency in real life?
Architecture (twin towers), U.S. Dept. of Treasury uses it to make money, Manufacturing

What is the difference between Congruent Figures and Similar Figures?
Congruent Figures – are the exact same shape and same size
Similar Figures – are the exact same size, but different sizes

Let’s take one last look… display transparency for ▲ABC
▲WYX.
Student Notes
7-5 Congruent Figures
Textbook 346 - 349
Figures that have:
the same shape AND the same size.
The corresponding angles and sides will have
the exact same measurements!
Congruent
Figures
Example
Symbol:
Identifying corresponding parts.
Corresponding Sides are the sides that “match-up” in two figures.
Corresponding Angles are the angles that “match-up” in two figures.
 Look at the figures and think to yourself, “How can I match-up these figures?”
B
E
C
F
 Use “arcs” to indicate which angles match-up.
 Use “tick” marks to indicate which sides match-up.
A
Naming Congruent figures.
You MUST write the angles in corresponding order.
Corresponding Angles
Corresponding Sides
A
D
BC
EF
B
____
CA
____
C
____
AB
____
Name the Congruent Figure:
ABC
_______
D
If you are given the congruency statement it is easy to match up the
corresponding sides and angles. It’s all about the ordering!
Complete the congruency statements given the following:
BAC
____
AB
____
CBA
____
ZX
▲ ABC
____
▲ XYZ
Name: _____________________
Date: ______________
Period: _______
Worksheet
Congruent Figures
1) ▲SHN ▲DAV are congruent. Which of the following statements is false? Explain why.
A. HSN
ADV
B. VAD
NHS
C. SH AV
D. HS AD
J
2) Answer the following questions regarding the congruent figures below.
I
A
C
B
H
Which angle is congruent to C? _____
Which angle is congruent to A? _____
Which angle is congruent to B? _____
3) ▲QVC
SNH
CVQ
QCV
4) LMNO
▲HSN are congruent.
_____
_____
_____
Which side is congruent to CA?
Which side is congruent to AB?
Which side is congruent to BC?
Complete each congruence statement.
NS
_____
VQ
_____
HN
_____
WZYX
Complete the following congruency statements:
L _____
Z _____
YX _____
YZ _____
NM _____
LO _____
O _____
MN _____
Y _____
N _____
XW _____
W _____
LM _____
ZW _____
_____
_____
_____
Classwork
5) These two right triangles are congruent.
Name 3 pairs of corresponding angles.
Name 3 pairs of corresponding sides.
_A___
_B___
_C___
_____
_____
_____
Side _AB__
Side _AC__
Side _BC__
_____
_____
_____
6) A math student concluded that the following two triangles were NOT congruent.
Why is the student correct? ___________________________________________________
3 in
9 in
7 in
14 in
7) The quadrilaterals below are congruent. Write congruency statements for each angle and each side.
A
B
E
F
C
D
_A____
_B____
_C____
_D____
_______
_______
_______
_______
G
Side __AB__
Side __BD__
Side __CD__
Side __AC__
H
Side_______
Side_______
Side_______
Side_______
8) Identifying congruent figures.
a) Define congruent figures:
b) Looking at the figures below which are congruent?
9) Which two figures below appear to be congruent? Explain why you think they are congruent.
Answer: Figures _____ and _____
Why?
Name: ___Answer Key________
Date: __________
Period: _______ Classwork
Worksheet
Congruent Figures
1) ▲SHN ▲DAV are congruent. Which of the following statements is false? Explain why.
A. HSN
ADV
B. VAD
NHS
C. SH AV
D. HS AD
Answer: C The verticies of congruent triangles are written in corresponding order.
Looking at the ordering of the letters, side SH does not match up to side AV.
2) Answer the following questions regarding the congruent figures below.
C
J
I
A
B
H
Which angle is congruent to C?
Which angle is congruent to A?
Which angle is congruent to B?
3) ▲QVC
SNH
CVQ
QCV
Answer: H
Answer: I
Answer: J
Which side is congruent to CA? Answer: HI
Which side is congruent to AB? Answer: IJ
Which side is congruent to BC? Answer: JH
▲HSN are congruent. Complete each congruence statement.
_____
VCQ
NS
_____ CV
_____
NSH
VQ
_____ SH
_____
HNS
HN
_____ QC
4) LMNO
WZYX
Complete the following congruency statements:
L _____
W
Z _____
YX _____ NO
YZ _____
NM _____ YZ
LO _____
O _____
X
MN _____
Y _____
N
N _____
XW _____ OL
W _____
LM _____ WZ
ZW _____
5) These two right triangles are congruent.
Name 3 pairs of corresponding angles.
Name 3 pairs of corresponding sides.
__A__
__D___
Side __AB___
__B___
__E___
Side __AC___
__C___
__F___
Side __BC___
M
NM
WX
ZY
Y
L
ML
__DE___
__DF___
__EF___
6) A math student concluded that the following two triangles were NOT congruent.
Why is the student correct? ___The corresponding sides of the triangles are different lengths.___
3 in
7 in
9 in
14 in
7) The quadrilaterals below are congruent. Write congruency statements for each angle and each side.
A
B
E
F
C
D
__A____
__B____
__C____
__D____
__E_____
__F_____
__G_____
__H_____
G
Side __AB____
Side __BD____
Side __CD____
Side __AC____
H
Side___EF____
Side___FH___
Side___GH___
Side___EG___
8) Identifying congruent figures.
a) Define congruent figures: Figures that have the same size and shape.
b) Looking at the figures below which are congruent? a, b, c, d are all congruent!
9) Which two figures below appear to be congruent? Explain why you think they are congruent.
Answer: Figures __1__ and __4__
Why? Looking at the grids, figures 1 and
4 appear to be the same size and shape.
Name: ________________
Period: _______
Congruent Figures
Use the congruent triangles on the right to answer the questions below. N
Write your answer in the blank provided beside each number.
_____ 1)
_____ 2)
_____ 3)
_____ 4)
Which angle is congruent to
A.
B.
C.
?
Which angle is congruent to
A.
B.
C.
?
Which angle is congruent to
A.
B.
C.
?
_____ 5)
B. PR
O
R
P
D.
D.
C. QR
______
D. RQ
Which segment is congruent to MO?
A. PR
_____ 6)
M
D.
Which would complete the congruence statement: ON
A. PQ
Q
B. RP
C. PQ
D. QR
Which would complete the congruence statement:
A. ∆QPR B. ∆PQR
C. ∆RPQ D. ∆RQP
∆MNO
______
7) Answer the following questions regarding the two congruent quadrilaterals below.
a)
b)
c)
d)
A
B
C
D
______
______
______
______
e) Side AD
f) Side CB
Side ______
Side ______
g) What is the length of Side AB? ______cm
Remember corresponding sides are equal! So, look at its
corresponding side on the other figure to get your answer!
See BACK!
Transformation Review
8)
Translate the ▲ABC Up 3 units, Left 5 units.
It is ok if the triangles end up overlapping!
9) a. Reflect ▲ABC across the y-axis.
b. Now, reflect ▲ABC over the x-axis.
A
B
Name the new coordinates of:
A
C
B
C
Name the coordinates of each new image:
over the y-axis
over the x-axis
A′ (______,______)
A′ (______,______)
A′ (______,______)
B′ (______,______)
B′ (______,______)
B′ (______,______)
C′ (______,______)
C′ (______,______)
C′ (______,______)
Name: Answer Key
Period: _______
Congruent Figures
Use the congruent triangles on the right to answer the questions below. N
Write your answer in the blank provided beside each number.
_____ 1)
_____ 2)
_____ 3)
_____ 4)
Which angle is congruent to
A.
B.
C.
?
Which angle is congruent to
A.
B.
C.
?
_____ 5)
B. PR
O
R
P
D.
D.
Which would complete the congruence statement: ON
C. QR
______
D. RQ
Which segment is congruent to MO?
A. PR
_____ 6)
M
D.
Which angle is congruent to
?
A.
B.
C.
A. PQ
Q
B. RP
C. PQ
D. QR
Which would complete the congruence statement: ∆MNO
A. ∆QPR
B. ∆PQR C. ∆RPQ D. ∆RQP
______
7) Answer the following questions regarding the two congruent quadrilaterals below.
a)
b)
c)
d)
A
B
C
D
______
______
______
______
e) Side AD
f) Side CB
W
X
Y
Z
Side ______
Side ______
WZ
YX
g) What is the length of Side AB? ______cm
9cm
Remember corresponding sides are equal! So, look at its
corresponding side on the other figure to get your answer!
See BACK!
Transformation Review
8)
Translate the ▲ABC Up 3 units, Left 5 units.
It is ok if the triangles end up overlapping!
9) a. Reflect ▲ABC across the y-axis.
b. Now, reflect ▲ABC over the x-axis.
A
B
Name the new coordinates of:
A
C
C
B
Name the coordinates of each new image:
over the y-axis
over the x-axis
A′ (–2, 9)
A′ (–3,6)
A′ (3, –6)
B′ (–2, 4)
B′ (–3, 1)
B′ (3, –1)
C′ (4, 4)
C′ (–9, 1)
C′ (9, –1)