AE=5 cm,EB=3 cm,BF=4 cm,AC=10 cm
FindEFandFC.
(Hint: Draw and label a picture, then draw another figure where the two triangles are shown separately.)
Answer:
3
8
=
EF
10
3
5
=
4
FC
or3
8
=
4
FC+ 4
EF= 3
3
4
cm FC= 62
3
cmSimilarity Transformations
Scale Factor Compared to Segment and Area Ratios – When a polygon is dilated using scale factork, the ratio
of the image of the segment to the original segment isk. This is true for the sides of the polygon, all the special
segments of triangles studied in chapter five, and the perimeter of the polygon. The relationship holds for any linear
measurement. Area is not a linear measurement and has a different scale factor. The ratio of the area of the image
to the area of the original polygons isk^2. Student frequently forget to square the scale factor when working with
the ratios of a figure and its image. This is an important concept that is frequently used on the SAT and on other
standardized tests.
Key Exercises:
4 ABChas coordinates at the following vertices.A( 1 , 13 ),B( 6 , 1 ), andC( 1 , 1 ).
- Graph 4 ABC.
- Use the distance formula to find the length of each side of 4 ABC.
- Calculate the perimeter of 4 ABC.
- Calculate the area of 4 ABC.
4 A[U+0080][U+0099]B[U+0080][U+0099]C[U+0080][U+0099]is the image of 4 ABCunder a dilation centered
at the origin with scale factor 3.
- Graph 4 A[U+0080][U+0099]B[U+0080][U+0099]C[U+0080][U+0099].
- Use the distance formula to find the length of each side of 4 A[U+0080][U+0099]B[U+0080][U+0099]C[U+0080][U+0099].
- Calculate the perimeter of 4 A[U+0080][U+0099]B[U+0080][U+0099]C[U+0080][U+0099].
- Calculate the area of 4 A[U+0080][U+0099]B[U+0080][U+0099]C[U+0080][U+0099].
Compare 4 A[U+0080][U+0099]B[U+0080][U+0099]C[U+0080][U+0099]to 4 ABC.
- What is the ratio of each set of corresponding side lengths, the perimeters, and the areas? What do you notice
when these ratios are compared to the scale factor.
Answers:
2.AC= 12 ,BC= 5 ,AB= 13
30
30
Chapter 2. Geometry TE - Common Errors