Do Now 1/10/12. Take out your HW from last night. Text p. 163, #1-4 all Copy HW in your planner. Text p. 164, #1-19 all, 23 &24 In your journal, use cross products to tell whether the ratios below are proportional (equal). 28 12. 16 6. 40 15. 3 8. 18 46. 8 9. 24 27. 42 18. ,. - PowerPoint PPT Presentation
Do Now 1/10/12 Do Now 1/10/12 Take out your HW from last night. Take out your HW from last night. Text p. 163, #1-4 all Text p. 163, #1-4 all Copy HW in your planner. Copy HW in your planner. Text p. 164, #1-19 all, 23 &24 Text p. 164, #1-19 all, 23 &24 In your journal, use cross products to tell In your journal, use cross products to tell whether the ratios below are proportional whether the ratios below are proportional (equal). (equal). 16 6 , 40 15 3 8 , 18 46 8 9 , 24 27 28 12 , 42 18 240 = 240; equal 138 = 144; not equal 216 = 216; equal 504 = 504; equal
Transcript
Do Now 1/10/12Do Now 1/10/12 Take out your HW from last night.Take out your HW from last night.
Text p. 163, #1-4 allText p. 163, #1-4 all
Copy HW in your planner.Copy HW in your planner. Text p. 164, #1-19 all, 23 &24Text p. 164, #1-19 all, 23 &24
In your journal, use cross products to tell whether the In your journal, use cross products to tell whether the ratios below are proportional (equal).ratios below are proportional (equal).
166
, 4015
38
, 1846
89
, 2427
2812
, 4218
240 = 240; equal
138 = 144; not equal
216 = 216; equal
504 = 504; equal
HomeworkHomeworkText p. Text p. 163, #1-4 all163, #1-4 all
PointPointposition in space position in space represented by a dot. represented by a dot.
AA
ZZ
DD
KK
LL
PlaPlanenea flat surface that extends on a flat surface that extends on
forever in all directions. forever in all directions.
How many planes on this figure?How many planes on this figure?
Line segmentLine segmentpart of a line with 2 endpoints and all the points in between.
C
D
E
FDC
EF
CD
FE
LinLinee a straight path extending a straight path extending
without end in 2 directions. without end in 2 directions.
RR
TTRT
ST
RS
SS
RayRayPart of a line that beginsPart of a line that beginsat a point and extends in one at a point and extends in one direction without ending. direction without ending.
AA
KK
AAKK
BB
ABABJKJK
JJ
CongruentCongruentTwo line segments are Two line segments are congruent when they are the congruent when they are the same length. same length.
CC DD EE FF
3EF
EFCD
33
AngleAngleTwo rays that begin at the Two rays that begin at the same point. same point.
CC
DD
EEVertexVertex
SidesSides
Naming Angles The following angle can be named in three ways:
BB
CCAA
BAC ACABVertexVertex
Objective
SWBAT use ratios to determine if two figures are similar
Two figures are Two figures are SIMILAR FIGURESSIMILAR FIGURES if they have if they have the the same shapesame shape but not necessarily the same but not necessarily the same size. The symbol ~ indicates two figures are size. The symbol ~ indicates two figures are similar. similar.
Two figures are similar if:Two figures are similar if:
1). The measures of their corresponding angles are equal 1). The measures of their corresponding angles are equal
2). The ratios of the lengths of their corresponding sides 2). The ratios of the lengths of their corresponding sides are proportional (equal ratios)are proportional (equal ratios)
DA FC AA
BB
CC
DD
EE
FF
Corresponding angles –Corresponding angles – matching angles of two figuresmatching angles of two figures
EB
When 2 angles have When 2 angles have the same measure, the same measure,
they are marked with they are marked with the same symbol or the same symbol or
measurement.measurement.
DEFABC ~
35°
35°
25°
25°
120°
120°
DE
AB
DF
AC
AA
BB
CC
DD
EE
FF
Corresponding sides –Corresponding sides –
matching sides of two figuresmatching sides of two figures
EF
BC
DEFABC ~
Given ABC ~ XYZ, name the corresponding angles and corresponding sides.
C
A
B
Y
Z
X
ZC
YB
XA
,
,SidesAngles
YZtoscorrespondCB
XZtoscorrespondAC
XYtoscorrespondAB
,
,
Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar.
A C
B
10 in
4 in 7 in D
E
F
16 in 28 in
40 in
AB corresponds to DE.
BC corresponds to EF.
ABDE
=? BCEF
=? ACDF
416
728
1040
14
14
14
Since the ratios of the corresponding sides are equivalent, the triangles are similar.
Write ratios using the corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
=? =?
AC corresponds to DF.
=? =?
Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar.
A C
B
8 in
3 in 7 in D
E
F
9 in 21 in
32 in
AB corresponds to DE.
BC corresponds to EF.
ABDE
=? BCEF
=? ACDF
39
721
832
13
13
14
Write ratios using the corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
=? =?
AC corresponds to DF.
=? =?
Since the ratios of the corresponding sides are not equivalent, the triangles are not similar.
With triangles, if the corresponding side lengths are all proportional, then the corresponding angles MUST have equal measures.
With figures that have 4 or more sides, if the corresponding side lengths are all proportional, then corresponding angles MAY or MAY NOT have equal measures.
QRST ~ ABCD because corresponding sides are proportional and corresponding angles are equal.
ABCD is not similar to WXYZ because corresponding sides are
proportional and but corresponding angles are NOT equal.
Tell whether the figures are similar.
The corresponding angles of the figures have equal measure.
Write ratios using corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
Since the ratios of the corresponding sides are equivalent, the figures are similar.
MNQR
=? NORS
=? OPST
=? MPQT
6 9=
? 812 =
? 4 6 =
? 1015
23
= 23
= 23
= 23
? ? ?
Substitute the length of the sides.
Simplify each ratio.
Since the ratios of the corresponding sides are equivalent, the figures are similar.
100 m
80 m
60 m 47.5 m80°
90°125°
65°M P
NO
400 m
320 m
190 m240 m
80° 65°
90°125°
Q T
R S
80 m
60 m 47.5 m
90°125°
NO
400 m
320 m
190 m240 m
80° 65°
90°125°
Q T
R S
The corresponding angles of the figures have equal measure.
Tell whether the figures are similar.
Write ratios using correspondingsides.
MNQR
=? NORS
=? OPST
=? MPQT
Write ratios using corresponding sides.
60240 =
? 80320 =
? 47.5190 =
? 100400
14
= 14
= 14
= 14
? ? ?
Try it outTry it outTell whether the figures are similar.
59°59°
35°35°
86°86°
119°
55°
107°
79°
107°
80°
135°
38°
NPQS
=? NOQR
=? PORS
714
48
612
12
12
12
=? =?
=? =?
Similar Not similar; corresponding angles do not have equal measures
HomeworkText p. 164, #1-19 all, 23 &24Text p. 164, #1-19 all, 23 &24
