8.4 similar triangles. number talk in chemistry class there is a girl to boy ratio of 5 : 8. if...
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8.4 Similar Triangles
Number Talk
In Chemistry Class there is a girl to boy ratio of 5 : 8. If there are a total of 39 students, how many boys are there?
The scale on a map is 6cm : 2kn. If the distance between two cities is 8kn, how far apart in cm are the two cities on the map?
In Geometry Class, the girl to boy ratio is 8 to 6. If there are a total of 42 students, how many girls are there?
How did we do?
Let’s Try
Similar Triangles Given the triangles are similar. Find the value of
the variable.
>
>
6
2
5
h
Left side of sm Δ Base of sm ΔLeft side of lg Δ Base of lg Δ=
h
5
8
6
6h = 40
6
40h
3
20h
∆ABC is similar to ∆DBE.
9
48
5
x
y
B
A
C
D
E
Agenda
Number talk expectations Number talk Warm up Discuss the Angle Angle Theorem
Number Talk
Name the rule!
Warm Up Given the triangles are similar. Find the value of the
variable.
)
)
))
))20
10
m
42
Postulate 25
Angle-Angle (AA) Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Determine whether the triangles are similar.
18
9
6
32°33°
No, because two angles of one triangle are not congruent to two angles of another triangle.
Determine whether the triangles are similar.
60°
Yes, because two angles of one triangle are congruent to two angles of another triangle.
60°
60°
60°
Decide whether two triangles are similar, not similar, or cannot be
determined.
92° 57°
92°
41°
A
A + 92 + 57 = 180A + 149 = 180 A = 31 31°
S
S + 92 + 41 = 180 S + 133 = 180 S = 47
47°Not similar
Given two triangles are similar, solve for the variables.
15
10
16
3
a
15
115a
10
a + 3 141516
2b - 8
)
)
15(a+3) = 10(16)15a + 45 = 16015a = 115
3
23a
2 Practice Problems
For each problem. Show your solutions mathematically as well as explain what you did in plain English.
For Example “When setting up the proportion 4/x = 15/5 I
knew that EB corresponds with DC and EA corresponds with AD.”
Take Exit Slip on IPAD
Test ID: 0881886769 Re Take Yesterday’s Formative: 6461882153