Similar Triangles Exploration
Similar shapes are shapes that have the same general shape but are different sizes. Use the applet below to explore the properties of similar shapes.
a. What relationships exist between the angle
measurements of similar shapes? Will similar shapes always follow this pattern?
The corresponding angles of similar shapes are always equal.
Yes, similar shapes always follow this pattern.
b. What relationships exist between the side length
measurements of similar shapes?
The ratios of corresponding side lengths in similar shapes
remain constant.
c. How can you use the scale factor between the shapes to
find an unknown length?
Multiply the known side length by the scale factor to find
an unknown length. Since the scale factor between triangles ABC and DEF is 2,
you can find an unknown length by multiplying a corresponding side from the
smaller triangle by 2.
d. How can you use the side length measurements of
similar shapes to calculate the scale factor?
Divide the length of one side of a shape by the
corresponding side length of the similar shape to find the scale factor. Divide
the length of a side in the larger triangle by the corresponding side in the
smaller triangle. Triangle DEF has a side of 5 units and the
corresponding side in Triangle ABC is 2.5 units, then: 5/2.5=2 This
means Triangle DEF is twice the size of Triangle ABC.
e. Consider the ratio of two side lengths of a triangle,
such as CB/AC. What is the value of this ratio? How does this ratio compare to
the ratio of corresponding side lengths on a similar shape, such as FE/DF?
The ratio CB/AC is equal to the ratio FE/DF, as
corresponding side ratios in similar shapes are always the same.