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