Transcript Les. 2 - Mr. K`s Virtual World of Math

Unit 1 Chapter 2 Lesson 2
Congruence
Pg. 107
Learn to use properties of congruent
figures to solve problems.
Vocabulary
correspondence
A correspondence is a way of matching up
two sets of objects.
If two polygons are congruent, all of their
corresponding sides and angles are
congruent.
Helpful Hint
Marks on the sides of a figure can be used
to show congruence.
__
__
AB @ QR (1 mark)
__ __
BC @ PR (2 mark)
__
__
AC @ PQ (3 mark)
Writing Congruent Statements
Write a congruence statement for each pair of
polygons.
The first triangle can be named
triangle ABC. To complete the
congruence statement, the vertices
in the second triangle have to be
written in order of the
correspondence.
55
55
The congruence statement is triangle ABC @ triangle QRP.
Try this!
Write a congruence statement for each pair of
polygons.
The first trapezoid can be named
trapezoid ABCD. To complete the
congruence statement, the vertices in
the second trapezoid have to be
written in order of the correspondence.
A
|
60°
120°
120°
T
Q
60°
D
|||
|||
|
B
60°
120°
C
R
120°
60°
S
The congruence statement is trapezoid ABCD @ trapezoid STQR.
Try this!
Write a congruence statement for each pair of
polygons.
110°
A
The vertices in the first pentagon are
110°
written in order around the pentagon
F 140°
starting at any vertex.
B
C
140°
110°
110° E
D
110°N
M
L
The congruence statement is
hexagon ABCDEF @ hexagon MNOPQL.
140°
110°
110°
140°
Q
110°
O
P
Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral VWXY @ quadrilateral JKLM.
Find a.
a + 8 = 24
–8
–8
a = 16
WX @ KL
Subtract 8 from both sides.
Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral VWXY @ quadrilateral JKLM.
Find b.
6b = 30
6b = 30
6
6
b=5
ML @ YX
Divide both sides by 6.
Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral VWXY @ quadrilateral JKLM.
Find c.
5c = 85
5c = 85
5
5
c = 17
J @ V
Divide both sides by 5.
Try This!
In the figure, quadrilateral JIHK @ quadrilateral QRST.
Find a.
H
3a
I
4b°
30°
K
R
J
Q
6
S
120°
c + 10°
T
Try This!
In the figure, quadrilateral JIHK @ quadrilateral QRST.
Find b.
H
3a
I
4b°
30°
K
R
J
Q
6
S
120°
c + 10°
T
Try This!
In the figure, quadrilateral JIHK @ quadrilateral QRST.
Find c.
H
K
3a
4b°
30°
I
90°
J
R
Q
6
S
90° 120°
c + 10°
T
Congruent Triangles
• We have learned about Congruent Polygons
– Congruency Statements lead to corresponding angles and
sides
– Congruent simply means the same size and shape
• We will now expand this to study Congruent Triangles
• We will use four acronyms……….
NOT THE OTHER TWO….
Congruent Triangles
• If two figures are exactly the same size
and shape, they are congruent.
• Two triangles are congruent if the
following corresponding parts of two
triangles are congruent.
–
–
–
–
•
•
Three Sides (SSS)
Two angles and the included side (ASA)
Two sides and the included angle (SAS)
Two angles then a side (AAS)
Video below if to show why SSA and AAA do not work
http://www.youtube.com/watch?v=DWWwo4l_s9g&feature=player_
embedded
Example
• Determine whether the triangles are congruent. If
so, write a congruence statement and tell why
D
B
C
A
E
Determine whether the triangles are congruent. If so, write
a congruence statement and tell why
S
P
J
M
K
L
Q
R
U
T
2 mm
Find the value of “x” in the following congruent triangle
60°
6 ft
(4x – 20)°
2 yds
Homework
• HC: pg.111-112 (1-5, 7-10)
• CC: pg. 111-112 (1-5, 7, 8, 10)
• www.ixl.com Q12
• Congruent Triangles Worksheet #1