Scale Ratios
scale images
similar polygons
Are these shapes similar?
Proving Triangles Similar
100
Write the scale ratio 5:4 as a fraction, decimal AND percent
5/4
1.25
125%
100
If I apply a scale factor of 80% on a shape, will that new shape be enlarged or reduced?
reduced (80% is 80/100 which is less than 1)
100
find angle R.
angle R= 50 degrees
100
What are the two things you must look for to confirm that two shapes are similar?
- corresponding angles=same
- corresponding sides= proportional (can apply same scale factor to all corresponding sids)
100
You have triangles ABC and XYZ and two corresponding angles are congruent in each. What is the reason they are similar?
What is AA similarity
200
Side AB= 5cm , side BC= 8cm, and side EF is 3cm. What scale factor was applied on triangle ABC, to create triangle DEF?
I/O= 3/8 or 0.375
200
Imagine you were asked to scale down a square of quilt fabric with a side length of 30 cm by using a scale ratio of 7:4.
Determine the new side length of the square? (round to whole number)
17cm
200
compare the shape NMLK with SRQP. Find all the pairs corresponding sides.
NM and SR
ML and RQ
LK and QP
KN and PS
200
Find the length of side X
x= 4.67
200
In triangles ABC and XYZ, AB = 9, BC = 12, AC = 15. XY = 15, YZ = 20, XZ = 25. Are the triangles similar? Write the similarity statement and reason.
What is ABC ~ XYZ by SSS similarity
300
A small box of height 13 cm and width 10 cm is similar to a large box of height 44 cm and width x. What is the measure of x? (round to a whole number)
34cm
300
Ms. F is 1.75m tall. If a student draws Ms. F to scale, where her height is drawn as 20cm, by what scale factor is Ms. F reduced? Express as a decimal
(first convert units!)
0.114
300
One cylinder has a radius of 25 cm and a height of 35 cm. Another cylinder has a radius of 30 cm and a height of 40 cm. Are the cylinders similar? Show your calculations.
Not similar
25/30 not the same as 35/40
300
A tree casts a shadow that is 8 meters long. At the same time, a 2-meter stick casts a shadow 1.5 meters long. How tall is the tree?
10.67 m
300
In triangles ABC and XYZ, angle A = angle X, AB =10, XY = 24, AC = 5 and XZ = 12. Are the triangles similar, Write the similarity statement and reason.
What is ABC ~ XYZ by SAS similarity
400
If the scale of a map of USA is 150km:1 cm, what distance (in km) would be represented by 2.15cm on the map?
322.5km
400
Suppose that I want a smaller and larger option for the size of a quilt. The original quilt has a side length of 24 cm.
What are the side lengths for a 60% scale and a 120% scale?
14.4 cm and 28.8 cm
400
Find the value of x, y and z.
x= 40
y=35
z=15
400
Compare triangle ABC with EDF. Are they similar?
Yes! angle B (60 degrees) corresponds with angle D (60 degrees)
angle D: 70+50=120. so 180-120=60 degrees.
400
You have triangles ABC and XYZ and angle A = angle Z and angle C = angle Y. What is the similarity statement of the triangles and reason?
What is ABC ~ ZXY by AA similarity
500
The display window of a furniture store has miniature version of some of the items the store sells. A table that is 240 cm long, 186 cm wide, and 120 cm high has been reduced in size and the miniature version is 40 cm long. Find the WIDTH of the miniature version.
width of miniature version: 31cm
500
Veronica was asked to scale a square of quilt fabric with a side length of 180 cm using a scale factor of 15%.
Determine the new side length of the square?
27 cm
500
If triangle A has one interior angle equal to 67 degrees. Triangle B, which is similar, has an interior angle equal to 82 degrees. Find all three interior angles in each triangle.
triangle A and B both have: (similar triangle all have same interior angles)
67, 82, 31
500
Find length x (always include units)
I/O: 5/8=7/x. cross multiply:
x= 11.2cm
500
In triangles ABC and XYZ, angle A = angle Z. AC = 50, AB =25, XZ =100 and XY =50. Are the triangles similar? If so, write the similarity statement and reason. If not, explain.
What is NO, They may not be similar because only one of the angles given is the included angle. It does not fit SAS similarity. Only if angle X = angle A then they are.