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1 ­ 4.3 Day 1 (student work).notebook
January 09, 2017
January 09, 2017
4.3 Congruent Triangles
I will find the values of variables and angle measures using properties of congruent polygons to successfully answer both "you try" examples on my own.
Do Now: Consider the pentagons below, where pentagon DGVLA → pentagon RKMCP by a reflection in line b.
1. Is a reflection a rigid (congruence) transformation?
D
2. Fill in the blanks:
A
G
a. MC ≅ _____
b. ∠K ≅ ______
c. KM ≅ ______
d. ∠A ≅ ______
e. DG ≅ ______
f. ∠R ≅ _____
g. AD ≅ ______
h. ∠L ≅ _____
i. PC ≅ ______
j. ∠V ≅ _____
b
L
V
C
P
M
K
R
HW:
• 4.3 Practice WS
• Unit 6 Quiz Jan. 19th
Congruent Polygons ‐ (section 4.3)
What does it mean for two segments to be congruent?
What does it mean for two angles to be congruent?
What does it mean for two polygons to congruent?
If one polygon can be mapped onto another polygon by a rigid transformation (or composition of rigid transformations), then the two polygons are congruent. Since rigid transformations preserve distances and angle measures, then all the corresponding sides and angles of the polygons are congruent.
1 ­ 4.3 Day 1 (student work).notebook
January 09, 2017
I will find the values of variables and angle measures using properties of congruent polygons to successfully answer both "you try" examples on my own.
Two geometric figures are congruent if they have exactly the same size and shape.
Two Ways to Determine if Polygons are Congruent:
1. If you are given/you can show that all corresponding sides and angles are congruent
2. If you are given/you can show that a composition of rigid transformations will map one polygon onto the other
1 ­ 4.3 Day 1 (student work).notebook
January 09, 2017
Intro WKST:
80
130
50
130
D
G
50
trapezoid ABCD ≅ trapezoid EFGH 100
100
F
C
80
A
E
a) Write a congruence statement B
for the pair of trapezoids.
H
*erase to reveal*
b) Identify all pairs of congruent corresponding parts.
A ≅ E
B ≅ F
C ≅ G
D ≅ H
*erase to reveal*
BC ≅ FG
AD ≅ EH
BA ≅ FE
CD ≅ GH
Intro WKST: In the diagram below, .
Complete the following statements.
a) Find x and y.
b) = _____ 45
c) Classify .
d) o
(5y)
(x ­ 7) cm
o
1 ­ 4.3 Day 1 (student work).notebook
January 09, 2017
I will find the values of variables and angle measures using properties of congruent polygons to successfully answer both "you try" examples on my own.
I will find the values of variables and angle measures using properties of congruent polygons to successfully answer both "you try" examples on my own.
In the previous example, F → _______ and point H → ______. Therefore, FH ≅ _____.
10
100 o
(
5 )o
K
45o The segment is congruent to itself.
This is an example of the ________________________ Property of Congruence.
1 ­ 4.3 Day 1 (student work).notebook
January 09, 2017
I will find the values of variables and angle measures using properties of congruent polygons to successfully answer both "you try" examples on my own.
Example 2: 1. Given: The two triangles are images of each
other after a reflection in IT.
I
a. Fill in the blank: IT ≅ _______ by the
Reflexive Property of Congruence.
b. Write a congruence statement: M
2. Given: The two triangles are images of each
other after a rotation about point H.
a. Fill in the blank: AB ≅ _____ by the
Reflexive Property of Congruence.
T
F
A
C
H
B
X
b. Write a congruence statement:
I will find the values of variables and angle measures using properties of congruent polygons to successfully answer both "you try" examples on my own.
Third Angles Theorem
congruent
If two angles of one triangle are _______ to two angles of a second triangle, then the 3rd angles
congruent
________ of the triangles are ________.
Example:
1 ­ 4.3 Day 1 (student work).notebook
January 09, 2017
I will find the values of variables and angle measures using properties of congruent polygons to successfully answer both "you try" examples on my own.
Example 2:
Find the value of x. Explain your reasoning.
I will find the values of variables and angle measures using properties of congruent polygons to successfully answer both "you try" examples on my own.
Example 2 (You Try!):
Find the value of x. Explain your reasoning.
1 ­ 4.3 Day 1 (student work).notebook
Example 3:
January 09, 2017
a) What else can be marked congruent? Explain. b) Are the triangles congruent? Yes or No? c) If yes, write a congruence statement.
*Erase to reveal answers!*
a) DB ≅ BD by Reflexive POC
b) Yes, all corr. parts are ≅.
Yes
c) ΔABD ≅ ΔCDB
a) Nothing else.
b) No, corr. sides are not ≅.
No
c) (none)
Example 3 (You Try!):
a) What else can be marked congruent? Explain. b) Are the triangles congruent? Yes or No? c) If yes, write a congruence statement.
*Erase to reveal answers!*
a) Q≅ Q by Third Angles Thm. or Reflexive POC
b) No, corr. sides are not ≅.
c) (none)
a) IJH ≅ LJK because they are vertical angles.
b) Yes, all corr. parts are ≅.
c) ΔHIJ ≅ ΔKLJ
1 ­ 4.3 Day 1 (student work).notebook
January 09, 2017
I will find the values of variables and angle measures using properties of congruent polygons to successfully answer both "you try" examples on my own.
Challenge!: In the diagram below, .
Part A. Find the value(s) of x.
o
(x2 + 6)
Part B. Which statements are false?
is an equilateral triangle.
o
(5x)