Proportional Parts - Petal School District
Transcript Proportional Parts - Petal School District
Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects
the other two sides in two distinct points, then it separates
these sides into segments of proportional lengths.
If BD AE ,
endpoints are the midpoints of two sides
Triangle Midsegment Theorem
A midsegment of a triangle is parallel to one side of the triangle,
and its length is one-half the length of that side.
Find x, BD, and AE.
If three or more parallel lines intersect two transversals,
then they cut off the transversals proportionally.
FJ GK HL
If two triangles are similar, then their perimeters are
proportional to the measures of the corresponding sides.
If ∆DEF ∼ ∆GFH, find the perimeter of ∆DEF.
Special Segments of Similar Triangles
If two triangles are similar, then the measures of the
corresponding altitudes, angle bisectors, and medians
are proportional to the measures of the corresponding sides.
In the figure, ∆EFD ~ ∆JKI. EG is a median of ∆EDF and
JL is a median of ∆JIK. Find JL if EF = 36, EG = 18, and
JK = 56.
EXAMPLE: The drawing below illustrates two poles supported by
wires. ∆ABC ~ ∆GED. AF CF and FG GC DC.
Find the height of pole EC.
An angle bisector in a triangle separates the opposite side into
segments that have the same ratio as the other two sides.
Find x if AB = 10, AD = 6, DC = x, and BC = x + 6.