Geometry Chapter 8
3 parallel lines intersect 2 transversals, divide transversals proportionally
3 parallel lines thm
a segment from a vertex to the midpoint of the opposite side
median
Two polygons are similar. The perimeter of the smaller polygon is ___ feet and the ratio of the corresponding side lengths is ___. Find the perimeter of the other polygon.
perimeter = _____ ; ratio for x
2 angles congruent, sim
AA sim thm
Sketch the triangles using the given description. Then determine whether the two triangles can be similar.
Ratio all sides, angle congruent (depends on theorems)
angle 1 congruent and lengths prop, sim
SAS sim thm
corr side lengths two prop, sim
SSS sim thm
ray bisects angle, divides ops side into segments whose lengths are prop to other 2 sides
Triangle Angle Bisector Theorem
a perpendicular segment from a vertex to the line containing the opposite side
altitude
The polygons are similar. The area of one polygon is given. Find the area of the other polygon
area = ___ (divide ratio multiply)
2 polygons = similar, ratio of perimeters = ratios of corr side lengths
areas of similar polygons
show triangles are similar
break down theorem, ratio triangles
if polygons similar, then ratio of 2 corr lengths = to sale factor of similar polygons
corresponding lengths in similar polygons
Show that the triangles are similar and write a similarity statement.
find out if similar, ratio sides (names) and triangles
use the diagram to complete the statement
if sim, name, if =, number
In the diagram, JKLM∼EFGH. Find the ratio of the perimeters of JKLM to EFGH
jklm/efgh (reverse reverse k)
Verify that △ABC∼△DEF. Find the scale factor of △ABC to △DEF
k
find the ratio of their perimeters
k
Find the scale factor of the figures. Then list all pairs of congruent angles. (abc to def)
k= def/abc, angle A = angle D etc, DE/AB etc
2 polygons sim, ratio perimeters = ratio of corr side lengths
permitters of similar polygons
Find the value of x for which PQ ∥ RS.
ratio (very carefully) for x
Decide whether the red and blue polygons are similar.
ratio and divide on calc
Identify a similarity statement for the two triangles.
ratio first to see if sim, if sim ratio tri
find the value of ____ that makes sim
ratio for x
Use the diagram to complete the proportion.
ratio to find other "half" (use names)
Find the length of AB
ratio to find side (use theorems)
Find the length of the indicated line segment.
ratio to find x
Find the value of the variable.
ratio to find x
Determine whether KM ∥ JN
ratio to verify parallelism
Determine whether the triangles are similar. If they are, select the correct similarity statement.
ratio tri names
triangles are sim, which is correct?
ratios with letters (side/side = side/side)
a line parallel to one side intersects 2 other sides, divides sides prop
triangle prop thm