Math 310

1
Math 310

• Section 10.4
• Similarity

2
Similar Triangles

• Def
• ?ABC is similar to ?DEF, written
  ?ABC ?DEF, iff ltA is congruent to ltD, ltB is
  congruent to ltE, ltC is congruent to ltF and AB/DE
  AC/DF BC/EF

3
Ex
The two following triangles are similar ?ABC
?DEF.
4
AA Property

• Thrm
• If two angles of one triangle are congruent,
  respectively, to two angles of a second triangle,
  then the triangles are similar. Denoted AA
• Note sometimes called the AAA property.

5
Ex
Are the two triangles similar? If they are find
the remaining sides.
6
Theorem 10-4

• Thrm
• If a line parallel to one side of a triangle
  intersects the other sides, then it divides those
  sides into proportional segments.

7
Ex
8
Ex
Suppose line DE is parallel to line segment BA in
triangle ABC. If ratio of BD to DC is 2/3 and CE
is length 3, what is the length of AE?
2
9
Theorem 10-5

• Thrm
• If a line divides two sides of a triangle into
  proportional segments, then the line is parallel
  to the third side.

10
Ex
Find the measures of all the interior angles of
triangle ABC.
35, 105 , 40
11
Theorem 10-6

• Thrm
• If parallel lines cut off congruent segments on
  one transversal, then they cut off congruent
  segments on any transversal.

12
Ex
Given the three lines are parallel, what is the
length of the segment next to the question mark?
7
13
Triangle Midsegment

• Def
• The midsegment of a triangle connects the
  midpoints of two adjacent sides of the triangle.

14
Midsegment Theorem

• Thrm
• The midsegment is parallel to the third side of
  the trianlge and half as long.

15
Ex
Given that JI is the midsegment of triangle FGH,
find all the interior angles of the triangle and
the length of the midsegment.
50, 60, 70, 4
16
Theorem 10-8

• If a line bisects one side of a triangle and is
  parallel to a second side, then it bisects the
  third side and therefore is a midsegment.

17
Ex
Is the segment JI the midsegment of triangle FGH?
18
Indirect Measurement

• One practical use of these theorems is the
  ability to measure objects and distances that
  would be impossible or impractical to do directly.

19
Ex
Book pg 689.