Ratios & Proportions
AA/SSS/SAS Similarity
Triangle Similarity
Proportions in Triangles
Mystery
Dilations
100
Solve for x:
x/32 = 4/5
x = 25.6
100
According to SSS Similarity, what do two triangles need to have in order to be similar?
All 3 corresponding ratios must be the same.
OR
All corresponding sides must be propotional.
100
Solve for x given that the triangles are similar.
x=8
100
Congruent triangles are always similar triangles.
True or False
True
100
Dialtion: J(4, 8), K(8, 8), L(4, 2), k =0.25, centered at the origin
J'(1, 2) K'(2, 2) L'(1, 0.5)
200
△ABC ~△DEF
Perimeter of △ABC=25u, AB=5u, DE=6u
What is the perimeter of △DEF?
Perimeter △DEF=30u
200
State if the triangles are similar or not and then what similarity statement makes it so.
YES, by AA Similarity
200
Complete the similarity statement.
Triangle DCB
200
Find y.
y=5
200
What is the measure of segment DE?
DE = 36
200
Dilation: 𝑇(−1, −3), 𝑈(−4, −4), 𝑉(−3, −2), 𝑘 =2, centered at T
T'(-1, -3) U'(-7, -5) V'(-5, -1)
300
Given two equilateral triangles with sides 16 and 20, respectively, the scale factor of the larger triangle to the smaller triangle (Hint: reduction or enlargement?)
16/20 = 4/5 = 0.2
300
State if the triangles are similar or not and then what similarity statement makes it so.
NO, not similar
300
Solve for x given △VUW~△SUT.
x=11
300
Find b.
b=30
300
Our geometry class went outside to measure the height of our school’s flagpole. A student who is 5.5 feet tall stands up straight and casts a shadow that is 11 feet long. At the same time a flagpole casts a shadow that is 36 feet long. Draw a diagram to represent the situation and determine the height of the flagpole.
height = 18ft
300
Dialtion: 𝑄(4, 0), 𝑅(−4, −4), 𝑇(−4, 2), 𝑘 =0.5, centered at R
Q'(0, -2) R'(-4, -4) T'(-4, -1)
400
Solve for x.
2/3 = (x+3)/(4x)
x=3
400
What is it called when the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of the other triangle and the included angle is congruent
SAS Similarity
400
(BE)/(EC)=?/(FC)
DF
400
Solve for "x".
x = 13.3 ft
400
The diagram is an example of this type of segment.
What is an Altitude?
400
dilation centered at the origin with a scale factor of 1.5 followed by a reflection in 𝑥 =−3 A(-3, 4) B(2, 2) C(-2, -4)
A"(-3, 7.5) B"(-9, 4.5) C"(-3, -6)
500
△ABC ~△DEF, find AC?
AC=7cm
500
State if the triangles are similar or not and then what similarity statement makes it so.
YES, by SAS Similarity
500
Are the triangles similar? If so, complete the similarity statement.
NOT SIMILAR
500
Given the angle bisector, solve for x.
x=5
500
Can you prove congruence? If so, write a triangle congruence statement and state which theorem you are using.
△DEF ≅ △HIG by ASA
500
rotation 90° counterclockwise about C followed by a dilation centered at C′ with a scale factor of 0.5 where A(-4, 5) B(2, 5) C(2, -2) D(-4, -2)
A"(-1.5, -5) B"(-1.5, -2) C"(2, -2) D"(2, -5)