aim: what is special about similar triangles?
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Aim: What is special about similar triangles?. Do Now:. In the diagram at right PQR ~ STU. Name the pairs of corresponding angles:. Q & T R & U P & S. 3. 9. 3. 3. 15. 12. QR. =. =. x. 2. y. TU. 10. 2. 2. =. =. Short cuts, anyone?. - PowerPoint PPT PresentationTRANSCRIPT
Course: Applied Geo. Aim: Similar Triangles
Aim: What is special about similar triangles?
Do Now:
In the diagram at right PQR ~ STU.
Name the pairs of corresponding angles:Q & T R & U P & S
P Q
R
12 cm
15 cm9 cm S
U
T
X
Y
10 cm
Course: Applied Geo. Aim: Similar Triangles
In the diagram at right PQR ~ STU.
A. Name the pairs of corresponding angles:Q & T R & U P & S
B. Name the pairs of corresponding sides:PQ & ST QR & TU PR & SU
C. Find the ratio of similitude between PQR and STU.D. Find the value of y. E. Find the value of x.
Problem #1
QRTU
= 1510
32
=
32
= 12y
P Q
R
12 cm
15 cm9 cm S
U
T
X
Y
10 cm
3y = 24y = 8 3
2= 9
x3x = 18
x = 6
Short cuts, anyone?
Course: Applied Geo. Aim: Similar Triangles
Similar TrianglesSimilar Triangles
Theorem 1:If the corresponding sides of two
triangles are in proportion, the triangles are similar.
Theorem 1:If the corresponding sides of two
triangles are in proportion, the triangles are similar.
Note: this is only true for triangles!!
Theorem 2:If two angles of one triangle are
congruent to two angles of a second triangle, then the two triangles are similar.
Two triangles are similar if
AA AA
Theorem 2:If two angles of one triangle are
congruent to two angles of a second triangle, then the two triangles are similar.
Two triangles are similar if
AA AA
Short cuts, anyone?
Course: Applied Geo. Aim: Similar Triangles
a. Explain why the two triangles are similar.
790
600410
790
b. Name the three pair of corresponding sides.
A
B C
W
M
E
AA AA
AB & EM, BC & MW, AC & EW
600
410
c. Name the three pair of corresponding angles.
A & E, B & M, C & W
Model Problem
Course: Applied Geo. Aim: Similar Triangles
Determine if the two triangles are similar.
1.3 in
0.8 in
Q
1.9 in
P
RH
0.4 in
G
1.0 in
0.7 in I
24.0
8.0
GH
PQ857.1
7.0
3.1
HI
QR
Since no angles are given we must determine if the sides are in proportion.
Because we have shown that two sides of the triangles are not in proportion, it is enough
then, to state that they are not similar.
Model Problem
Course: Applied Geo. Aim: Similar Triangles
Explain why the triangles are similar
R
V
BS
W
450
450
WSR VSB because vertical angles are congruent
R V because their measures are equal
RSW VSB because triangles are similar is two angles of the triangles are congruent AA AA
Model Problem
Course: Applied Geo. Aim: Similar Triangles
x m. 6 m.3 m.
The lengths, in meters, of the sides of a triangle are 24, 20, and 12. If the longest
sides of a similar triangle is 6 meters, what is the length of the shortest side?
24 m.
20 m.
12 m.
2. Because they are similar, corresponding sides are in proportion
1. Draw a picture
x
m
m
m .
.
. 12
6
24
24x = (6)(12) = 72
x = 3
Model Problem
Course: Applied Geo. Aim: Similar Triangles
PJ is 6-ft. tall. He casts a shadow that is four feet long. A nearby tree of unknown height casts a shadow of 30 feet. How tall is the tree?
PJ’s ht. 6 ft.
PJ’s shadow - 4 ft.
ft
ft
ft
x
4
30
6
4
180
4
4
x
1803064 x
Tree Height
x
Tree’s shadow 30 ft.
x = 45 feet
451
2
1 ~ 21 ~ 2