Shape Conjectures
All squares are similar. State truth or false and explain why. If false give a counterexample.
TRUE: All squares have 4 equal sides and 4 right angles
AC = 12
BC = 15
AB = 22
AC' = 96
BC' = 120
AB' = 176
See slide 6:
See Slide 7:
Are dilations a rigid or non-rigid transformation?
Non-rigid
All equilateral triangles are similar. State true or false and explain why. If false provide a counterexample.
TRUE: All equilateral triangles have 3 equal sides and 3 angles of 60 degrees
Angles are the same
Side lengths are proportional
If we have side lengths (provided below) with a scale factor of 3/5 what are our new side lengths?
AB = 20
AC = 35
BC = 55
AB' = 12
AC' = 21
BC' = 33
See slide 2:
See slide 3:
If we have Triangle ABC with side lengths (provided below), draw this example and dilate a new triangle with a scale factor of 2:
Rough estimates are okay! No need to be exact
AB = 3 cm
AC = 4 cm
BC = 5 cm
Check examples:
AB' = 6 cm
AC' = 8 cm
BC' = 10 cm
All isosceles triangles are similar. State true or false and explain why. If false state a counterexample.
FALSE: Although all isosceles triangles have 2 equal sides they do not have the same angles.
Counterexample:
50 50 80 <-- Angle measures
70 70 40 <-- Angle measures
Fill in the missing side lengths and state what the scale factor is:
AB = 42
AB' = 7
AC =
AC' = 12
BC = 88
BC' =
AC = 72
BC' = 14 & 2/3
Scale factor = 1/6
See slide 8:
See slide 9:
If we have triangle ABC with side lengths (provided below), draw this triangle and dilate a new one with a scale factor of 1/3.
AB = 12 cm
AC = 15 cm
BC = 33 cm
Check examples:
AB' = 4 cm
AC' = 5 cm
BC' = 11 cm
All rhombuses are similar. State true or false and explain why. If false provide a counterexample.
FALSE: All rhombuses have equal sides, but angles can differ.
Counterexample:
90 90 90 90 <-- Angle measures
60 120 60 120 <-- Angle measures
Fill in the missing side lengths and state the scale factor:
AB = 1.4
AC = 5.22
BC =
AB' = 3.5
AC' =
BC' = 18.4
BC = 7.36
AC' = 13.05
Scale factor = 2.5 or 2 & 1/2
See slide 10:
See slide 11:
Name 4 things that change when you dilate:
Size
Side Lengths
Perimeter
Area
Distance from center
All rectangles are similar. State true or false and explain why. If false provide a counterexample.
FALSE: Although all rectangles have 4 right angles, their side lengths can be different proportions and is the only thing used to determine similarity.
Counterexample:
A 2x4 rectangle and 3x5 rectangle
Find the missing side lengths and scale factor:
XY = 1.6
YZ =
XZ = 6.5
XY' = 5.12
YZ' = 21.696
XZ' =
Scale factor = 3.2
YZ = 6.78
XZ' = 20.8
See slide 4:
See slide 12:
CLOSEST GROUP GETS 500 POINTS!!!
Check examples